ICALP'97: Abstracts of Accepted Papers

Approximation results for the optimum cost partition problem
by Klaus Jansen

In this paper, we study the optimum cost chromatic partition (OCCP) problem for several graph classes. The OCCP problem is the problem of coloring the vertices of a graph such that adjacent vertices get different colors and that the total coloring costs are minimum.
We prove several approximation results for the OCCP problem restricted to bipartite, chordal, comparability, interval, permutation, split and unimodular graphs. We prove that there exists no polynomial approximation algorithm with ratio O(|V|^{0.5-\epsilon}) for the OCCP problem restricted to bipartite and interval graphs, unless P = NP.
Furthermore, we propose approximation algorithms with ratio O(|V|^{0.5}) for bipartite, interval and unimodular graphs. Finally, we prove that there exists no polynomial approximation algorithm with ratio O(|V|^{1-\epsilon}) for the OCCP problem restricted to split, chordal, permutation and comparability graphs, unless P=NP.

Efficiency of Asynchronous Systems and Read Arcs in Petri Nets
by Walter Vogler

Two solutions to the MUTEX-problem are compared w.r.t. their temporal efficiency. For this, a formerly developed efficiency-testing for asynchronous systems is adapted to nets with so-called read arcs. The close relation between efficiency-testing and fair behaviour is pointed out, and it is shown that read arcs are necessary for any solution to the MUTEX-problem.

On the concentration of the height of binary search trees
by John Michael Robson

The expectation of the absolute value of the difference between the heights of two random binary search trees of n nodes is less than 6.25 for infinitely many n. Given a plausible assumption, this expectation is less than 4.96 for all but a finite number of values of n.

Recursive Computational Depth
by James Lathrop, Jack Lutz

In the 1980's, Bennett introduced computational depth as a formal measure of the amount of computational history that is evident in an object's structure. In particular, Bennett identified the classes of weakly deep and strongly deep sequences, and showed that the halting problem is strongly deep. Juedes, Lathrop, and Lutz subsequently extended this result by defining the class of weakly useful sequences, and proving that every weakly useful sequence is strongly deep.
The present paper investigates refinements of Bennett's notions of weak and strong depth, called recursively weak depth (introduced by Fenner, Lutz and Mayordomo) and recursively strong depth (introduced here). It is argued that these refinements naturally capture Bennett's idea that deep objects are those which ``contain internal evidence of a nontrivial causal history.'' The fundamental properties of recursive computational depth are developed, and it is shown that the recursively weakly (respectively, strongly) deep sequences form a proper subclass of the class of weakly (respectively, strongly) deep sequences. The above-mentioned theorem of Juedes, Lathrop, and Lutz is then strengthened by proving that every weakly useful sequence is recursively strongly deep. It follows from these results that not every strongly deep sequence is weakly useful, thereby answering a question posed by Juedes.

An Algebra-Based Method to Associate Rewards with EMPA Terms
by Marco Bernardo

We present a simple method to associate rewards with EMPA terms in order to make the specification and the computation of performance measures easier. The basic idea behind this method is to specify rewards inside actions of EMPA terms, so it substantially differs from methods based on modal logic. The main motivations of this method are its ease of use as well as the possibility of defining a notion of equivalence which relates terms having the same reward, thus allowing for simplification without altering the performance index. We prove that such an equivalence is a congruence finer than the strong extended Markovian bisimulation equivalence, and we present its axiomatization.

The Word Matching Problem Is Undecidable For Finite Special String-Rewriting Systems That Are Confluent
by Paliath Narendran, Friedrich Otto

We present a finite, special, and confluent string-rewriting system for which the word matching problem is undecidable. Since the word matching problem is the non-symmetric restriction of the word unification problem, this presents a non-trivial improvement of the recent result that for this type of string-rewriting systems, the word unification problem is undecidable (Otto 1995). In fact, we show that our undecidability result remains valid even when we only consider very restricted instances of the word matching problem.

The name discipline of uniform receptiveness
by Davide Sangiorgi

In a process calculus, we say that a name x is {\em uniformly receptive} for a process P if: (1) at any time P is able of offering an input at x, at least as long as there are processes that could send messages at x; (2) the input offer at x is functional, that is, all messages received by P at x are applied to the same continuation. In the \pi-calculus this discipline is employed, for instance, when modeling functions, objects, higher-order communications, remote-procedure calls. We formulate the discipline of uniform receptiveness by means of a type system, and then we study its impact on behavioural equivalences and process reasoning. We develop some theory and proof techniques for uniform receptiveness, and illustrate their usefulness on some non-trivial examples.

Independent sets in asteroidal triple-free graphs
by Hajo Broersma, Ton Kloks, Dieter Kratsch, Haiko Mueller

An asteroidal triple is a set of three vertices such that there is a path between any pair of them avoiding the closed neighborhood of the third. A graph is called AT-free if it does not have an asteroidal triple. We show that there is an O(n^4) time algorithm to compute the maximum weight of an independent set for AT-free graphs. Furthermore we obtain O(n^4) time algorithms to solve the independent dominating set and the independent perfect dominating set problem on AT-free graphs. We also show how to adapt these algorithms such that they solve the corresponding problem for graphs with bounded asteroidal number in polynomial time. Finally we observe that the problems clique and partition into cliques remain NP-complete when restricted to AT-free graphs.
Keywords: algorithms, graphs, asteroidal triple, independent set

Computation Paths Logic: An Expressive, yet Elementary, Process Logic
by David Harel, Eli Singerman

A new process logic, is defined, called computation paths logic (CPL), which treats formulas and programs essentially alike. CPL is a pathwise extension of PDL in the spirit of the logic R of Harel and Peleg. It enjoys most of the advantages of previous process logics, yet is decidable in elementary time. We also offer extensions for modeling asynchronous/synchronous concurrency and infinite computations.

The Minimum Color Sum of Bipartite Graphs
by Amotz BarNoy, Guy Kortsarz

The problem of minimum color sum of a graph is to color the vertices of the graph such that the sum (average) of allassigned colors is minimum. Recently, it was shown that finding a polynomial approximation to this problem in general graphs is NP-hard. In the same paper, a 9/8-approximation algorithm was presented for bipartite graphs. The hardness question for this problem on bipartite graphs was left open. In this paper we show that the minimum color sum problem for bipartite graphs admits no polynomial approximation scheme, unless P=NP. The proof is by L-reducing this problem to the problem of finding the maximum independent set in a graph whose maximum degree is four. This result indicates clearly that the minimum color sum problem is much harder than the traditional coloring problem which is trivially solvable in bipartite graphs. As for the approximation ratio, we make a further step towards finding the precise threshold. We present a polynomial 10/9-approximation algorithm. Our algorithm uses a flow procedure in addition to the maximum independent set procedure used in previous results. KEYWORDS: Sum Coloring, Approximation Algorithms, L-Reduction, Bipartite Graphs.

Results on Resource-Bounded Measure
by Harry Buhrman, Stephen Fenner, Lance Fortnow

We construct an oracle relative to which NP has p-measure 0 but D has measure 1 in EXP. This gives a strong relativized negative answer to a question posed by Lutz. Secondly, we give strong evidence that BPP is small. We show that BPP has p-measure 0 unless EXP = MA and the polynomial-time hierarchy collapses. This contrasts with the work of Regan et. al., where it is shown that P/poly does not have p-measure 0 unless exponentially strong pseudorandom generators do not exist.

Recognizability Equals Definability for Partial k-Paths
by Valentine Kabanets

If a graph property is expressible in a counting monadic second-order logic (CMS), then the family of partial k-trees that satisfy this property can be recognized by a finite tree automaton. Courcelle conjectured that the converse implication also holds. The cases of k<=3 have been proved.
We show that every recognizable family oof partial k-paths is definable in CMS for any k. Thus, we establish that the expressive power of finite automata equals that oof logic on the class of partial k-paths. A by-product of our solution is the formula in a monadic second-order logic that defines the class of all partial k-paths for every k. This means that the obstruction set of each such class is computable.

Termination of Constraint Logic Programs
by Salvatore Ruggieri

In the general case, the lifting of termination proof methods from logic programming up to the CLP Scheme is not a trivial task, since in many real CLP systems declarativity is lost due to an incorrect operational semantics. In this paper, we introduce a method for proving universal termination of constraint logic programs by strictly extending the approach of Apt and Pedreschi [AP90]. Taking into account a generic constraint domain instead of the standard Herbrand univers, acceptable (CLP) programs are defined. We prove correctness and completeness of the method w.r.t. the leftmost selection rule for the class of ideal constraint systems, including CLP({\cal R}_{lin}), CLP({\cal RT}), and CLP({\cal FT}) among the others. However, many real systems are not ideal. We specifically design sufficient conditions for termination of CLP({\cal R}) programs, by pointing out how the underlying insights can be extended to other systems.

A Complete and Efficiently Computable Topological Classification of D-dimensional Linear Cellular Automata over Z_m.
by Giovanni Manzini, Luciano Margara

We study the dynamical behavior of D-dimensional linear cellular automata over Z_m. We provide easy-to-check necessary and sufficient conditions for a D-dimensional linear cellular automata over Z_m to be sensitive to initial conditions, expansive, strongly transitive, and equicontinuous. This paper completes the work initiated in [3] where transitivity and ergodicity were proved to be equivalent and exactly characterized. As a consequence of our results, we have a complete and efficiently computable topological classification of D-dimensional linear cellular automata over Z_m according to the most important dynamical properties studied in the theory of discrete time dynamical systems.

Enumerative sequences of leaves in rational trees
by Frederique Bassino, Marie-Pierre Beal, Dominique Perrin

We prove that any N-rational sequence of nonnegative integers satisfying the Kraft strict inequality for an integer k is the enumerative sequence of leaves by height of a rational k-ary tree. Particular cases of this result had been previously proved. We give some partial results in the equality case.

A completion algorithm for codes with bounded synchronization delay
by Veronique Bruyere

We show that any rational code with bounded synchronization delay is included in a rational maximal code with bounded synchronization delay.
KEYWORDS: automata formal languages variable-length codes combinatorics on words

On modular properties of higher order extensional lambda calculi
by Roberto Di Cosmo, Neil Ghani

We prove that confluence and strong normalisation are both modular properties for the addition of algebraic term rewriting systems to Girard's F^{\omega} equipped with either \beta-equality or \beta\eta-equality. The key innovation is the use of \eta-expansions over the more traditional \eta-contractions.
We then discuss the difficulties encountered in generalising these results to type theories with dependent types. Here confluence remains modular, but results concerning strong normalisation await further basic research into the use of \eta-expansions in dependent type theory.

Worst-case hardness suffices for derandomization: a new method for hardness-randomness trade-offs
by Alexander Andreev, Andrea Clementi, Jose Rolim

Up to now, the known derandomization methods have been derived assuming average-case hardness conditions. In this paper, we instead present the first worst-case hardness conditions sufficient to obtain P=BPP. Our conditions refer to the worst-case circuit complexity of Boolean operators computable in time exponential in the input size. Such results are achieved by a new method that departs significantly from the usual known methods based on pseudo-random generators. Indeed, we prove new particular bounds on the circuit complexity of partial Boolean functions which are then used to derive efficient constructions of hitting sets generators. As recently proved, such generators can derandomize any BPP-algorithm. Our method also gives a worst-case hardness condition for the circuit complexity of Boolean operators computable in NC (with respect to their output size) to obtain an efficient reduction from any two-side error NC algorithm into a zero-error NC algorithm thus obtaining ZNC=BPNC.

The expressibility of languages and relations by word equations
by Juhani Karhumaeki, Wojciech Plandowski, Filippo Mignosi

We prove theorems which allow to show that certain properties of words are not expressible as components of solutions of word equations. In particular, "the primitiveness" and "the equal length" are such properties, as well as being "any word over a proper subalphabet".

Constructive Linear Time Algorithms for Branchwidth
by Hans Bodlaender, Dimitrios Thilikos

Let {\cal G}_{k} be the class of graphs with branchwidth at most k. In this paper we prove that one can construct, for any k, a linear time algorithm that checks if a graph belongs in {\cal G}_{k} and, if so, outputs a branch decomposition of minimum width. Moreover, we find the obstruction set for {\cal G}_{3} and, for the same class, we give a safe and complete set of reduction rules. Our results lead to a practical linear time algorithm that checks if a graph has branchwidth \leq 3 and, if so, outputs a branch decomposition of minimum width.

Model Checking the Full Modal Mu-Calculus for Infinite Sequential Processes
by Olaf Burkart, Bernhard Steffen

In this paper we develop a new elementary algorithm for model-checking infinite sequential processes, including \emph{context-free processes}, \emph{pushdown processes}, and \emph{regular graphs}, that decides the full modal mu-calculus. Whereas the actual model checking algorithm results straightforwardly from considering conditional semantics together with backtracking caused by alternation, the corresponding correctness proof requires a stronger framework, which uses \emph{dynamic environments} modelled by finite-state automata.

Finite loops recognize exactly the regular open languages
by Martin Beaudry, Francois lemieux, Denis Therien

In this paper, we characterize exactly the class of languages that are recognizable by finite loops, i.e. by cancellative binary algebras with an identity. This turns out to be the well-studied class of regular open languages. Our proof technique is interesting in itself: we generalize the operation of block product of monoids, which is so useful in the associative case, to the situation where the left factor in the product is non-associative.

Solving Trace Equations Using Lexicographical Normal Forms
by Volker Diekert, Yuri Matiyasevich, Anca Muscholl

Very recently, Matiyasevich showed that the question whether an equation over a trace monoid has a solution or not is decidable. In his proof this question is reduced to the solvability of word equations with constraints, by induction on the size of the commutation relation. In the present paper we give another proof of this result using lexicographical normal forms. Our method is a direct reduction of a trace equation system to a word equation system with regular constraints. We use for this a new result on lexicographical normal forms.

Randomization and nondeterminism are incomparable for ordered read-once branching programs
by Farid Ablayev

In [2] we exhibited a simple boolean functions f_n in n variables such that:
1) f_{n} can be computed by polynomial size randomized ordered read-once branching program with one sided small error; 2) any nondeterministic ordered read-once branching program that computes f_n has exponential size.
In this paper we present a simple boolean function g_n in n variables such that: 1) g_n can be computed by polynomial size nondeterministic ordered read-once branching program; 2) any two-sided error randomized ordered read-once branching program that computes f_n has exponential size.
These mean that BPP and NP are incomparable in the context of ordered read-once branching program.

On confluence in the pi-calculus
by Anna Philippou, David Walker

An account of the basic theory of confluence in the pi-calculus is presented, useful techniques for showing confluence of complex mobile systems are given, and the utility of some of the theory presented is illustrated via an analysis of a distributed algorithm.

Maintaining Minimum Spanning Trees in Dynamic Graphs
by Monika Rauch Henzinger, Valerie King

We present the first fully dynamic algorithm for maintaining a minimum spanning tree in time o(\sqrt n) per operation. To be precise, the algorithm uses O(n^{1/3} \log^2 n) amortized time per update operation. The algorithm is fairly simple and deterministic. We also present the first fully dynamic deterministic algorithm for maintaining connectivity (and, as a consequence, bipartiteness) in amortized time O(n^{1/3} \log n) per update, with O(1) worst-case time per query.

A Semantically Sound Actor Tranlsation
by Ian Mason, Carolyn Talcott

In this paper we present two actor languages: a high level User Language and a low level Kernel Language. The user language is object-oriented. Actors qua objects have methods and synchronization constraints which allow an object to control when a method can be invoked. The kernel language is an extension of a simple functional language with primitives for actor computation. Each of the languages is given a simple operational semantics via a labelled transition system, and an abstract interaction semantics derived from the computations of the transition system. The main result presented here is a translation from the user language to the kernel language and a proof that this mapping preserves the interaction semantics. This demonstrates that the basic actor primitives of the kernel are as expressive as those of the user language, although perhaps less convenient from a programmers point of view. The proof itself is of interest since it demonstrates a methodology based on abstract actor structures for proving correctness of transformations and translations of actor languages and more generally of concurrent object languages.

Improving Spanning Trees by Upgrading Nodes
by Sven Krumke, Madhav Marathe, Hartmut Noltemeier, Ramamurthy Ravi, SS Ravi, Ravi Sundaram, Hans-Christoph Wirth

We study budget constrained optimal network upgrading problems. Such problems aim at finding optimal strategies for improving a network under some cost measure subject to certain budget constraints. A general problem in this setting is the following. We are given an edge weighted graph G=(V,E) where nodes represent processors and edges represent bidirectional communication links. The processor at a node v can be upgraded at a cost of c(v). Such an upgrade reduces the delay of each link emanating from v. The goal is to find a minimum cost set of nodes to be upgraded so that the resulting network has the best performance with respect to some measure. We consider the problem under two measures, namely, the weight of a minimum spanning tree and the bottleneck weight of a minimum bottleneck spanning tree. We present approximation and hardness results for the problem. Our results are tight to within constant factors. We also show that these approximation algorithms can be used to construct good approximation algorithms for the dual versions of the problems where there is a budget constraint on the upgrading cost and the objectives are minimum weight spanning tree and minimum bottleneck weight spanning tree respectively.

An improved master theorem for divide-and-conquer recurrences
by Salvador Roura

We present a new master theorem for the study of divide-and-conquer recursive definitions, which improves the old one in several aspects. In particular, it provides more information, frees us from technicalities like floors and ceilings, and covers a wider set of toll functions and weight distributions, stochastic recurrences included.

Upper bound on communication complexity of private information retrieval
by Andris Ambainis

We construct a scheme for private information retrieval with k databases and communication complexity O(n^{1/(2k-1)}).

Axiomatizations for the Perpetual Loop
by Wan Fokkink

Milner proposed an axiomatization for the Kleene star in basic process algebra, in the presence of deadlock and empty process, modulo bisimulation equivalence. In this paper, Milner's axioms are adapted to no-exit iteration x*delta, which executes x infinitely many times in a row, and it is shown that this axiomatization is complete for no-exit iteration in basic process algebra with deadlock and empty process, modulo bisimulation.

Star-free picture expressions are strictly weaker than first-order logic
by Thomas Wilke

We exhibit a first-order definable picture language which we prove is *not* expressible by any star-free picture expression, ie, it is not star-free. Thus first-order logic over pictures is strictly more powerful than star-free picture expressions are. This is in sharp contrast with the situation with words: the well-known McNaughton-Papert theorem states that a word language is expressible by a first-order formula if and only it is expressible by a star-free (word) expression.
The main ingredients of the non-expressibility result are a Fraisse style algebraic characterization of star freeness for picture languages and combinatorics on words.

Colouring Paths in Directed Symmetric Trees with Applications to WDM Routing
by Luisa Gargano, Pavol Hell, Stephane Perennes

Let T be a symmetric directed tree, i.e., an undirected tree with each edge viewed as two opposite arcs. We prove that the minimum number of colours needed to colour the set of all directed paths in T, so that no two paths of the same colour use the same arc of T, is equal to the maximum number of paths passing through an arc of T. This result is applied to solve the all-to-all communication problem in wavelength--division--multiplexing (WDM) routing in all--optical networks, that is, we give an efficient algorithm to optimally assign wavelengths to the all the paths of a tree network. Moreover, we study conditions for a given set S of paths be coloured efficiently with the minimum possible number of colours/wavelengths. It is known that the problem of colouring a general subset of all possible paths in a symmetric directed tree is an NP-hard problem.

A Primal-Dual Approach to Approximation of Node-Deletion Problems for Matroidal Properties
by Toshihiro Fujito

This paper is concerned with the polynomial time approximability of node-deletion problems for hereditary properties. It has been known that when such a graph property has only a finite number of minimal forbidden graphs the corresponding node-deletion problem can be efficiently approximated to within some constant factor of the optimum. On the other hand when there exist infinitely many minimal forbidden graphs no constant factor approximation has been known except for the case of the Feedback Vertex Set (FVS) problem in undirected graphs.
We will focus on such properties that are derived from matroids definable on the edge set of any graph. It will be shown first that all the node-deletion problem for such properties can be uniformly formulated by a simple but non-standard form of the integer programming. The primal-dual approximation algorithm for all such problems is then presented based on this formulation and the dual of its linear programming relaxation. The performance ratios implied by this approach will be analyzed and given in terms of the combinatorial structures underlying the problems of interest.
It will be shown next, as an application of the current primal-dual approach, that the FVS problem is not the sole exceptional case; i.e., there exist other graph (hereditary) properties with an infinite number of minimal forbidden graphs, for which the node-deletion problems are efficiently approximable to within a factor of 2, the best constant factor known for either Vertex Cover or FVS. In fact, we will show, there are infinitely many of them. Such properties are derived from the notion of matroidal families of graphs and relaxing the definitions for them. The infinite sequence of these properties will be constructed with those for both VC and FVS problems at its basis and thus providing a proper generalization of them. It will be also indicated that our formulation for these node-deletion problems introduces the integrality gap of at most 2 unlike the more natural "covering" formulations for them.

Bisimulation for probabilistic transition systems: a coalgebraic approach
by Erik de Vink, Jan Rutten

The notion of bisimulation as proposed by Larsen and Skou for discrete probabilistic transition systems is shown to coincide with a coalgebraic definition in the sense of Aczel and Mendler in terms of a set functor, which associates to a set its collection of simple probability distributions. This coalgebraic formulation makes it possible to generalize the concepts of discrete probabilistic transition system and probabilistic bisimulation to a continuous setting involving Borel probability measures. A functor M_1 is introduced that yields for a metric space its collection of Borel probability measures. Under reasonable conditions, this functor exactly captures generalized probabilistic bisimilarity. Application of the final coalgebra paradigm to M_1 then yields an internally fully abstract semantical domain with respect to probabilistic bisimulation, which is therefore well-suited for the interpretation of probabilistic specification and stochastic programming concepts.

Some bounds on the computational power of Piecewise Constant Derivative systems
by Olivier Bournez

We study the computational power of Piecewise Constant Derivative (PCD) systems. PCD systems are dynamical systems defined by a piecewise constant differential equation. They can be seen as computational machines working on a continuous space with a continuous time. We show that the computation times of these machines can be measured either as a discrete value, called ``the discrete time'', or either as a continuous value, called ``the continuous time''. We prove that PCD systems are equivalent to Turing machines and to linear machines in finite discrete time. We prove that the languages recognized by PCD systems in dimension d in finite continuous time are precisely the languages of the d-2 ^{th} level of the arithmetical hierarchy. Hence we have a precise characterization of the computational power of PCD systems and we solve a problem left open by a [Asarin and Maler,95]

On recognizable and rational formal power series in partially commuting variables
by Manfred Droste, Paul Gastin

Kleene's theorem on the coincidence of regular and rational languages in free monoids has been generalized by Sch\"utzenberger to a description of the recognizable formal power series in non-commuting variables over arbitrary semi-rings, and by Ochma\'nski to a characterization of the recognizable languages in trace monoids. Here we will describe the recognizable formal power series over arbitrary semi-rings and in partially commuting variables, i.e. over trace monoids. We prove that the recognizable series are certain rational power series, which can be constructed from the polynomials by using the operations sum, product and a restricted star which is applied only to series for which the elements in the support all have the same connected alphabet. The converse is true if the underlying semi-ring is commutative. It is shown that these assumptions are necessary. This provides a joint generalization of both Sch\"utzenberger's and Ochma\'nski's theorems.

On a conjecture of J. Shallit
by Julien Cassaigne

We solve a conjecture of J. Shallit related to the automaticity function of a unary language, or equivalently to the first occurrence function in a symbolic sequence. The answer is negative: the conjecture is false, but it can be corrected by changing the constant involved. The proof is based on a study of paths in the Rauzy graphs associated to the sequence.

Symbolic Model Checking for Probabilistic Processes
by Christel Baier, Ed Clarke, Vassili Hartonas-Garmhausen, Marta Kwiatkowska, Mark Ryan

We introduce a symbolic model checking procedure for Probabilistic Computation Tree Logic (PCTL) and its generalization PCTL^* over labelled Markov chains as models. Model checking for probabilistic logics typically involves solving linear equation systems as means to ascertain the probability of a given (non-probabilistic) formula holding in a state. Our algorithm is based on the idea of representing the matrices used in the linear equation systems in terms of an appropriate generalization of Binary Decision Diagrams (BDDs) called Multi-Terminal Binary Decision Diagrams (MTBDDs) introduced in Clarke et al [CFGMYZ93], and combining that with BDD-based model checking. To enable precise probability calculation for path formulas we use the standard construction of the Rabin automaton (via Vardi \& Wolper construction of the Buchi automaton followed by Safra's determinization) for an LTL formula and, as suggested by de Alfaro [Alf96], construct the product of thus obtained automaton with the Markov chain model. Expressing these standard constructions as BDDs avoids explicit state space construction, thus yielding an efficient model checking procedure.

On-line Routing in All-Optical Networks
by Yair Bartal, Stefano Leonardi

The paper deals with on-line routing in WDM optical networks. A sequence of communication requests arrives over time, each is a pair of nodes to be connected by a path. The problem is to assign a wavelength and a path to each pair, so that no two paths sharing a link are assigned the same wavelength. The goal is to minimize the number of wavelengths necessary to establish all connections.
We consider trees, trees of rings, and meshes topologies, previously studied in the off-line case. We give on-line algorithms with logarithmic competitive ratio for all these topologies. We give a matching lower bound for meshes, and an almost matching lower bound for trees.

Minimizing Diameters of Dynamic Trees
by Stephen Alstrup, Jacob Holm, Kristian de Lichtenberg, Mikkel Thorup

In this paper we consider an on-line problem related to minimizing the diameter of a dynamic tree T. A new edge f is presented, and our task is to delete the edge e of the induced cycle so as to minimize the diameter of the resulting tree. Starting with a tree with n nodes, we show how each such best swap can be found in worst-case O(log^2 n) time. The problem was raised by Italiano and Ramaswami in ICALP'94, where they gave an algorithm which use O(n)-time to process each new edge.

Checking Properties of Polynomials
by Bruno Codenotti, Funda Ergun, Peter S. Gemmell, S. Ravi Kumar

In this paper we show how to construct efficient checkers for programs that claim to compute properties of polynomials. The properties we consider are roots, norms, and other analytic/algebraic functions of polynomials. We show how to check a program \Pi that computes a specific root (e.g., the largest) or a subset of roots of a given polynomial p which is available as a black box. The checkers, in addition to never computing the root(s) themselves, strive to minimize both the running time (preferably o(deg^2 (p))) and the number of black box evaluations of p (preferably o(deg (p))). We obtain deterministic checkers when a separation bound between the roots is known and probabilistic checkers when the roots can be arbitrarily close.
We then extend the checkers to handle the situations when the program \Pi returns an approximation to the root and when the evaluation of the polynomial p is approximate. Our results translate into efficient checkers for matrix spectra computations both in the exact and approximate settings, operating in the library model of [BLR93]. Next we show that the usual characterization of norms using the triangle inequality is not suited for self-testing in the exact case, but surprisingly, could be used in the approximate case.
Our results are complementary to most of the existing results on testing polynomials. The testers in the latter have the goal of determining whether a program computes a polynomial of given degree, whereas we are interested in checking the properties of a given polynomial. The nature of these properties entails the use of techniques that are new to checking from several disciplines like numerical and complex analysis, geometry, and in particular, geometry of polynomials.

Exact Analysis of Dodgson Elections: Lewis Carroll's 1876 Voting System is Complete for Parallel Access to NP
by Edith Hemaspaandra, Lane Hemaspaandra, Joerg Rothe

In 1876, Lewis Carroll proposed a voting system in which the winner is the candidate who with the fewest changes in voters' preferences becomes a Condorcet winner---a candidate who beats all other candidates in pairwise majority-rule elections. Bartholdi, Tovey, and Trick provided a lower bound---NP-hardness---on the computational complexity of determining the election winner in Carroll's system. We provide a stronger lower bound and an upper bound that matches our lower bound. In particular, determining the winner in Carroll's system is complete for parallel access to NP, i.e., it is complete for the class Theta_2, for which it becomes the most natural complete problem known. It follows that determining the winner in Carroll's elections is not NP-complete unless the polynomial hierarchy collapses. We note that, in contrast with our Theta_2 completeness result, for each fixed integer k there is a polynomial-time algorithm to compute the election winner, in Carroll's system, for elections having at most k candidates.

The Equivalence Problem for Deterministic Pushdown Automata is Decidable
by Geraud Senizergues

The equivalence problem for deterministic pushdown automata is shown to be decidable. We exhibit a complete formal system for deducing equivalent pairs of deterministic rational series on the alphabet associated with a dpda M.

Distributed Processes and Location Failures
by James Riely, Matthew Hennessy

Site failure is an essential aspect of distributed systems; nonetheless its effect on programming language semantics remains poorly understood. To model such systems, we define a process calculus in which processes are run at distributed locations. The language provides operators to kill locations, to test the status (dead or alive) of locations, and to spawn processes at remote locations. Using a variation of bisimulation, we provide alternative characterizations of strong and weak barbed congruence for this language, based on an operational semantics that uses configurations to record the status of locations. We then derive a second, symbolic characterization in which configurations are replaced by logical formulae. In the strong case the formulae come from a standard propositional logic, while in the weak case a temporal logic with past time modalities is required. The symbolic characterization establishes that, in principle, barbed congruence for such languages can be checked efficiently using existing techniques.

Efficient Array Partitioning
by Sanjeev Khanna, S. Muthukrishnan, Steven Skiena

We consider the problem of partitioning an array of n items into p intervals so that the maximum weight of the intervals is minimized. The currently best known bound for this problem is O(np). In this paper, we present two improved algorithms for this problem: one runs in time O(n+p^2(\log n)^2) and the other runs in time O(n\log n). The former is optimal whenever p \leq \sqrt{n}/\log n, and the latter is near-optimal for arbitrary p.
We consider the natural generalization of this partitioning to two dimensions, where an n \times n array of items is to be partitioned into p^2 blocks by partitioning the rows and columns into p intervals each and considering the blocks induced by this partition. The problem is to find that partition which minimizes the maximum weight among the resulting blocks. This problem is known to be NP-Complete. Here we provide a simple, polynomial time algorithm that determines a solution at most O(1) times the optimum; the previously best approximation ratio was O(\sqrt{p}).
Both the results above are proved for the case when the weight of an interval or block is the sum of the elements in it. These problems arise in load balancing for parallel machines and data partitioning in parallel languages. Applications in motion estimation by block matching in video and image compression, give rise to the dual problem, that of minimizing the number of dividers p so that the maximum weight of a block is at most \delta. We give an O(\log n) approximation algorithm for this problem.
All our results for two dimensional array partitioning extend to any higher fixed dimension.

Dynamic algorithms for graphs of bounded treewidth
by Torben Hagerup

The formalism of monadic second-order (MS) logic has been very successful in unifying a large number of algorithms on graphs of bounded treewidth. We extend the elegant framework of MS logic from static problems to dynamic problems, in which queries about MS properties of a graph of bounded treewidth are interspersed with updates of vertex and edge labels. This allows us to unify and occasionally strengthen a number of scattered previous results obtained in an ad-hoc manner and to enable solutions to a wide range of additional problems to be derived automatically.
As an auxiliary result of independent interest, we dynamize a data structure of Chazelle and Alon and Schieber for answering queries about sums of labels along paths in a tree with vertices labeled by elements of a semigroup.

Constructing Big Trees from Short Sequences
by Peter Erdos, Michael Steel, Laszlo Szekely, Tandy Warnow

The construction of evolutionary trees is a fundamental problem in biology. All current polynomial time methods (to our knowledge) are unlikely to recover the topology of the true tree from sequences of realistic lengths (bounded, perhaps, by 10,000 nucleotides) for large sets of widely divergent sequences, even if such methods are known to be able to reconstruct the correct topology given long enough sequences. Therefore, all current polynomial time methods may be incapable of addressing difficult and important data sets such as the {\em Tree of Life}. We address this problem and present a new polynomial time algorithm for reconstructing evolutionary trees called the {\em Short Quartets Method}. Our method computes topologies of subtrees induced by ``short" quartets, which avoid the problematic influence of pairs of widely divergent sequences. We reconstruct a tree on the entire set of sequences from these inferred subtrees when they are compatible. We describe a simple implementation of this method based upon applying the four-point method to derived distances, and study its convergence rate for the Cavender-Farris model of evolution. We show that for each fixed range of the mutation probabilities associated to the model tree, our method has a convergence rate that is at worst polynomial, while it is polylogarithmic for typical trees. In STOC '96, Farach and Kannan studied a method for inferring Cavender-Farris trees, and have recently extended their analysis to include the convergence rate for the topology estimation; their analysis shows that their method may require superpolynomial length sequences to obtain accurate topologies with high probability. Consequently, this indicates that our method will produce the correct topology from shorter sequences than can be guaranteed for the Farach-Kannan method. We also compare our method to an exact algorithm for the L_{\infty}-nearest tree, and show that on any input for which the exact algorithm can be guaranteed to be correct, so can ours. We use the probabilistic method and show that our method requires only polylogarithmic length sequences for random trees, for each fixed range of the mutation rates. We extend our method to the reconstruction of more general r-state model trees. \old{ In recent years, the focus of attention in the mathematical side of systematic biology has switched from proofs of consistency to studies of the convergence rates of different methods with respect to accurate estimation of the topology of the model tree, under the assumption that the sequences are generated by a stochastic process on an evolutionary tree, and assuming that each site evolves i.i.d. Because of the connection between these stochastic models of evolution and additive trees, all reasonable distance based methods are consistent (i.e. converge on the true tree given adequate length sequences). In this paper we study the performance of two distance-based methods, the 3-approximation algorithm of Agarwala et al (SODA '96) for the L_{\infty}-nearest tree, and a new method we propose, Short Quartet Method. We derive analytical bounds for these methods on the rate at which the sequence length must grow as a function of the number of species and the associated parameters of the tree in order to obtain the topology of the model tree with high probability. Almost all previous studies have been empirical, so that our results are the first to directly provide analytical guarantees of the topology estimation. However, we will also discuss the extensions of Farach and Kannan to their analysis of the 3-approximation algorithm of Agarwala et al, since their original study was concerned with a related but different problem (the convergence of their method in terms of the variational distance). For each method, we provide a formula establishing an upper bound on the sequence length needed to obtain a correct estimation of the topology, so that each formula involves only the number of sequences, the range within which the mutation rates on the edges must lie, and either the depth or the diameter of the model tree. We use the probabilistic method to show that the depth of almost all trees (under either the uniform or the Yule-Harding distributions) grows significantly slower than the diameter. This establishes that the Short Quartets Method requires significantly shorter sequences than the other methods to obtain the topology of the model tree with high probability, independent of the mutation probabilities on the edges. In particular, we show that the sequence length needed by the Short Quartets Method is always at worst polynomial, while the length needed by the other two methods can be superpolynomial. We show briefly how our analysis can be extended to the more biologically relevant a-state models. ae establish a lower bound of \log n on the sequence length needed to obtain an accurate topology estimation using any method (deterministic or randomized). It follows that for many model trees, the upper bounds we obtain on the sequence lengths needed for recovering the topology of almost all trees (independent of edge mutation probabilities) are polynomial in the lower bound.

On Characterization of Escrow Encryption Schemes
by Yair Frankel, Moti Yung

Designing escrow encryption schemes is an area of much recent interest. Due to its importance to governments and business organizations it may become crucial to the design and deployment of cryptographic systems. However, the basic design issues, characterizations and difficulties of escrow systems are not fully understood or specified at the moment. Escrow encryption differs from a typical encryption system since: (1) there are two potential receivers (the actual receiver and law enforcement which may selectively open encrypted message for crime prevention); (2) there is, therefore, a need for ``on-line assurance (verification) of 'compliance' with the specification'' to guarantee that a potential law-enforcement receiver will indeed get the message upon escrow; and (3) there is a need to assure compliance of law enforcement (e.g., to avoid framing of honest users).
Without a theoretical underpinning of the concept, we are not well equipped to design solid escrow schemes or to understand where are the difficulties. The goal of this paper is to characterize one aspect of escrow encryption schemes, namely their requirements of ``compliance''. We model public-key escrow systems formally, based on available requirements. We then show that basic escrow schemes with certain necessary requirements are related (in fact, equivalent) to schemes with certain security levels that have been extensively investigated by theoretical cryptography.
We show that the combination of on-line compliance assurance by the sender and two different receivers (intended receiver and potential law-enforcement) in the context of escrow encryption system is equivalent to a ``chosen ciphertext secure public-key system'' (i.e., one secure against an adversary who has access to a decryption oracle before trying to decipher a target ciphertext). If we further add measures that will force law enforcement to comply as well -- namely, if we require messages to be associated with a ``context'' (which may include the sender, the receiver and a time unit), as well as opening of messages to law enforcement only within a given (authorized) context, then we obtain a system equivalent to what is known as ``non-malleable encryption schemes''. The reductions of the known secure schemes to their escrow-related schemes are quite direct and reduce the ``security parameter'' in a linear factor at most, showing a strong proximity between the systems. The characterization also leads us to design schemes that exploit or emanate from the equivalence.
key words: Escrow encryption system models, compliance and compliance verification, law enforcement, secure public-key schemes, chosen ciphertext security, non-malleable security, characterization of cryptosystems.

Tilings and quasiperiodicity
by Bruno Durand

Quasiperiodic tilings are those tilings in which finite patterns appear regularly in the plane. This property is a generalization of the periodicity; it was introduced for representing quasicrystals and it is also motivated by the study of quasiperiodic words. We prove that if a tile set can tile the plane, then it can tile the plane quasiperiodically ---a surprising result that does not hold for periodicity. In order to compare the regularity of quasiperiodic tilings, we introduce and study a quasiperiodicity function and prove that it is of the form x \mapsto x +c if and only if the considered tiling is periodic. At last, we prove that if a tile set can be used to form a quasiperiodic tiling which is \emph{not} periodic, then it can form an uncountable number of tilings.

On Explicit Substitution and Names
by Eike Ritter, Valeria de Paiva

Calculi with explicit substitutions have found widespread acceptance as a basis for abstract machines for functional languages. In this paper we investigate the relations between variants with de Bruijn-numbers, with variable names, with reduction based on raw expressions and calculi with equational judgements. We show the equivalence between these variants, which is crucial in establishing the correspondence between the semantics of the calculus and its implementations.

Efficient Parallel Graph Algorithms For Coarse Grained Multicomputers and BSP
by Edson Caceres, Frank Dehne, Afonso Ferreira, Paola Flocchini, Ingo Rieping, Allesandro Roncato, Nicola Santoro, Siang Song

In this paper, we present deterministic parallel algorithms for the coarse grained multicomputer (CGM) and BSP which solve the following well known graph problems: (1) list ranking, (2) Euler tour construction, (3) computing the connected components and spannig forest, (4) lowest common ancestor preprocessing, (5) tree contraction and expression tree evaluation, (6) computing an ear decomposition or open ear decomposition, (7) 2-edge connectivity and biconnectivity (testing and component computation), and (8) cordal graph recognition (finding a perfect elimination ordering). The algorithms for Problems 1-7 require O(log p) communication rounds and linear sequential work per round. Our results for Problems 1 and 2 hold for arbitrary ratios n/p, i.e. they are fully scalable, and for Problems 3-7 it is assumed that n/p >= p^\epsilon, \epsilon > 0, which is true for all commercially available multiprocessors.
We view the algorithms presented as an important step towards the final goal of O(1) communication rounds. Note that, the number of communication rounds obtained in this paper is independent of n and grows only very slowly with respect to p. Hence, for most practical purposes, the number of communication rounds can be considered as constant. The result for Problem 1 is a considerable improvement over those previously reported. The algorithms for Problems 2-7 are the first practically relevant parallel algorithms for these problems for commercially available coarse grained parallel machines.

An abstract data type for real numbers
by Pietro Di Gianantonio

We present a calculus having real numbers as a basic data type. The calculus is defined by its denotational semantics. We prove the universality of the calculus. We show how the definition of an operational semantics is problematic. We discuss this problem and present a possible solution.
keywords: real number computability, domain theory, denotational and operational semantics, abstract data types

Molecular Computing, Bounded Nondeterminism, and Efficient Recursion
by Richard Beigel, Bin Fu

The maximum number of strands used is an important measure of a molecular algorithm's complexity. This measure is also called the space used by the algorithm. We show that every NP problem that can be solved with b(n) bits of nondeterminism can be solved by molecular computation in a polynomial number of steps, with four test tubes, in space 2^{b(n)}. In addition, we identify a large class of recursive algorithms that can be implemented using bounded nondeterminism. This yields improved molecular algorithms for important problems like 3-SAT, independent set, and 3-colorability.

The Geometry of Orthogonal Reduction Spaces
by Zurab Khasidashvili, John Glauert

We investigate mutual dependencies of subexpressions of a computable expression, in orthogonal rewrite systems, and identify conditions for their independent computation, concurrently. To this end, we introduce concepts familiar from ordinary Euclidean Geometry (such as basis, projection, distance, etc.) for reduction spaces. We show how a basis at an expression can be constructed so that any reduction starting from that expression can be decomposed as the sum of its projections on the axes of the basis. To make the concepts computationally more relevant, we relativize them w.r.t. stable sets S of results (such as the set of normal forms, head-normal forms, and weak-head-normal forms, in the Lambda Calculus), and show that an optimal concurrent computation of an expression w.r.t. S consists of optimal computations of its S-independent subexpressions. All these results are obtained for Stable Deterministic Residual Structures, which are Abstract Reduction Systems with an axiomatized residual relation, and model all orthogonal rewrite systems.

Discrete-time control for rectangular hybrid automata
by Thomas A. Henzinger, Peter W. Kopke

The main contribution of this paper is the realization that the discrete-time control of continuous-time systems not only is often a more adequate model of reality than continuous-time control, but is amenable to algorithmic methods for a much wider class of systems. While continuous-time controllers can be synthesized automatically only for timed automata, we show that discrete-time, or sampling, controllers can be synthesized automatically for all rectangular hybrid automata.
Rectangular hybrid automata model digital control programs of analog plant environments. We study rectangular hybrid automata where the plant state evolves continuously in real-numbered time, but the controller samples the plant state and changes the control state discretely, only at the integer points in time. We prove that rectangular hybrid automata have finite bisimilarity quotients when all control transitions happen at integer times, even if the contraints on the derivatives of the variables vary between control states. This is sharply in contrast with the conventional model where control transitions may happen at any real time, and already the reachability problem is undecidable. Based on the finite bisimilarity quotients, we give an exponential algorithm for the symbolic sampling-controller synthesis of rectangular automata. We show our algorithm to be optimal by proving the problem to be EXPTIME-hard. We also show that rectangular automata form a maximal class of systems for which the sampling-controller synthesis problem can be solved algorithmically.

The Theory of Vaccines
by Massimo Marchiori

Despite the major role that modularity occupies in computer science, all the known results on modular analysis only treat particular problems, and there is no general unifying theory. In this paper we provide such a general theory of modularity. First, we study the space of the criteria for modularity (the so-called modularity space), and give results on its complexity. Then, we introduce the notion of vaccine and show how it can be used to completely analyze the modular space. It is also shown how vaccines can be effectively used to solve a variety of other modularity problems, providing the best solutions. As an application, we successfully apply the theory to the study of modularity for term rewriting, giving for the first time optimality results, and completely solving the modularity problem for the major properties of rewriting.
KEYWORDS: term rewriting, modularity, optimality, program verification, program development.

Refining and Compressing Abstract Domains
by Roberto Giacobazzi, Francesco Ranzato

In the context of Cousot and Cousot's abstract interpretation theory, we present a general framework to define, study and handle operators modifying abstract domains. In particular, we introduce the notions of operators of refinement and compression of abstract domains: A refinement enhances the precision of an abstract domain; a compression
operator (compressor) can exist relatively to a given refinement, and it simplifies in the best possible way a domain for that refinemen t. The adequateness of our notions is shown by the fact that most of the existing operators on abstract domains falls in our framework (e.g., the well-known refinement of reduced product and the corresponding compressor of complementation). A precise relationship of adjunction between refinements and compressors is also given, justifying why compressors can be understood as inverses of refinements.

Constrained Bipartite Edge Coloring with Applications to Wavelength Routing
by Christos Kaklamanis, Pino Persiano, Thomas Erlebach, Klaus Jansen

Motivated by the problem of efficient routing in all-optical networks, we study a constrained version of the bipartite edge coloring problem. We show that if the edges adjacent to a pair of opposite vertices of an L-regular bipartite graph are already colored with \alpha L different colors, then the rest of the edges can be colored using at most (1+\alpha/2)L colors. We also show that this bound is tight by constructing instances in which (1+\alpha/2)L colors are indeed necessary. We also obtain tight bounds on the number of colors that each pair of opposite vertices can see.
Using the above results, we obtain a polynomial time greedy algorithm that assigns proper wavelengths to a set of requests of maximum load L per directed fiber link on a directed fiber tree using at most 5/3L wavelengths. This improves previous results of [ragh,focs,esa,eric].
We also obtain that no greedy algorithm can in general use less than 5/3L wavelengths for a set of requests of load L in a directed fiber tree, and thus that our algorithm is optimal in the class of greedy algorithms which includes the algorithms presented in [ragh,focs,esa,eric].

Periodic and Non-periodic Min-Max Equations
by Uwe Schwiegelshohn, Lothar Thiele

In this paper we address min-max equations for periodic and non-periodic problems. In the non-periodic case a simple algorithm is presented to determine whether a graph has a potential satisfying the min-max equations. This method can also be used to solve a more general min-max problem on periodic graphs. Also some results regarding the uniqueness of solutions in the periodic case are given. Finally, we address a more general quasi periodic problem and provide an algorithm for its solution.

Bisimulation equivalence is decidable for one-counter processes
by Petr Jancar

It is shown that bisimulation equivalence is decidable for the processes generated by (nondeterministic) pushdown automata where the pushdown behaves like a counter, in fact. Also regularity, i.e. bisimulation equivalence with some finite-state process, is shown to be decidable for the mentioned processes.

Game Theoretic Analysis of Call-by-value Computation
by Kohei Honda, Nobuko Yoshida

We present a general semantic universe of call-by-value computation based on elements of game semantics, and validate its appropriateness as a semantic universe by the full abstraction result for call-by-value PCF, a generic typed programming language with call-by-value evaluation. The key idea is to consider the distinction between call-by-name and call-by-value as that of the structure of information flow, which determines the basic form of games. In this way the call-by-name computation and call-by-value computation arise as two independent instances of sequential functional computation with distinct algebraic structures. We elucidate the type structures of the universe following the standard categorical framework developed in the context of domain theory. Mutual relationship between the presented category of games and the corresponding call-by-name universe is also established.

A Complete Characterization of the Path Layout Construction Problem for ATM Networks with Given Hop Count and Load
by Tamar Eilam, Michele Flammini, Shmuel Zaks

We investigate the time complexity of deciding the existence of layouts of virtual paths in high-speed networks, that enable a connection from one vertex to all others, that have maximum hop count h and maximum edge load l, for a stretch factor of one. We prove that the problem of determining the existance of such layouts is NP-complete for every given values of h and l except for the cases h=2, l=1 and h=1, any l, for which we give polinomial-time layout constructions. Extensions for cases of a stretch factor greater than one are also discussed.

Randomness-Efficient Non-Interactive Zero-Knowledge
by Alfredo De Santis, Giovanni Di Crescenzo, Giuseppe Persiano

The model of Non-Interactive Zero-Knowledge allows to obtain minimal interaction between prover and verifier in a zero-knowledge proof if a public random string is available to both parties. In this paper we investigate upper bounds for the length of the random string for proving one and many statements, obtaining the following results:
\begin{itemize} \item We show how to prove in non-interactive perfect zero-knowledge any polynomial number of statements using a random string of fixed length, that is, not depending on the number of statements. Previously, such a result was known only in the case of computational zero-knowledge, and for all languages in NP. First we give a protocol for the language of quadratic non residuosity, and then a protocol for a general class of languages, which we call Simulator-Rankable languages, which we show to include all known languages having a non-interactive perfect zero-knowledge proof system. \item Under the quadratic residuosity assumption, we show how to prove any NP statement in non-interactive zero-knowledge on a random string of length O(nk), where n is the size of the statement and k is the security parameter, which improves the previous best construction by a factor of O(k). \end{itemize}

On the Dynamics of Sharing Graphs
by Andrea Asperti, Cosimo Laneve

It has been recently conjectured by several authors that the number of fan-annihilations in Lamping's optimal reduction algorithm can provide a reasonable lower bound to the ``intrinsic'' computational complexity of lambda-terms. In this paper, we show how to describe fan annihilations in terms of statics, giving a precise and simple description of these operations as suitable paths in the initial term. As a corollary, we bring more evidence to the above mentioned conjecture, proving that the complexity of a typical environment machine (Krivine machine) cannot be better than the number of fan-annihilations in Lamping's algorithm.

Symbolic Reachability Analysis of FIFO Channel Systems with Nonregular Sets of Configurations
by Ahmed Bouajjani, Peter Habermehl

We address the verification problem of FIFO-channel systems. We apply the symbolic analysis principle to these systems. We represent their sets of states (configurations) using structures called CQDD's combining finite-state automata with constraints on number of occurrences of symbols. These constraints are expressed in Presburger arithmetics. We show that CQDD's allow forward and backward reachability analysis of systems with nonregular sets of configurations. Moreover, we prove that CQDD's allow to compute the exact effect of the repeated execution of any fixed cycle in the transition graph of a system. We use this fact to define a generic reachability analysis semi-algorithm parametrized by a set of cycle \Theta. Given a set of configurations, this semi-algorithm performs a least fixpoint calculation to construct the set of its successors (or predecessors). At each step, this calculation is accelerated by considering the cycles in \Theta as additional ``meta-transitions'' in the transition graph, generalizing the approach adopted in [BG96].

Efficient Splitting and Merging Algorithms for Order Decomposable Problems
by Roberto Grossi, Giuseppe F. Italiano

Let S be a set whose items are sorted with respect to d>1 total orders \prec_1, \ldots, \prec_d, and which is subject to dynamic operations, such as insertions of a single item, deletions of a single item, split and concatenate operations performed according to any chosen order \prec_i (1 \leq i \leq d). This generalizes to dimension d>1 the notion of concatenable data structures, such as 2--3--trees, which support splits and concatenates under a single total order. The main contribution of this paper is a general and novel technique for solving order decomposable problems on S, which yields new and efficient concatenable data structures for dimension d>1. By using our technique we maintain S with the following time bounds: O(\log p) for the insertion or the deletion of a single item, where p is the number of items currently in S; O(p^{1-1/d}) for splits and concatenates along any order; O(p^{1-1/d}) plus an output sensitive cost for rectangular range queries. The space required is O(p). We provide several applications of our technique. First, we present new multidimensional data structures implementing two--dimensional priority queues, two--dimensional search trees, and concatenable interval trees: these data structures allow us to improve many previously known results on decomposable problems under split and concatenate operations, such as membership query, minimum--weight item, range query, and convex hulls. Second, and perhaps a bit surprisingly, we reduce some dynamic graph problems to order decomposable problems. Finally, we show how to make our technique for decomposable problems suitable for efficient external memory implementation.

Basic Observables for Processes
by Michele Boreale, Rocco De Nicola, Rosario Pugliese

A general framework is proposed that can be used to define behavioural preorders over processes by considering the context closures with respect to basic observables. These provide information about the initial communication capabilities of processes and about their possibility of engaging in an infinite internal chattering. After presenting the general framework, we concentrate on a CCS-like language and show that some of the observables-based precongruences do correspond to behavioural preorders longly studied in the literature. In particular, we exhibit alternative (observables-based) characterizations for the must preorder of De Nicola and Hennessy and for the fair must preorder introduced by Brinksma, Rensink and Vogler and by Cleaveland and Natarajan. The coincidence proofs shed light on the differences between must and fair must preorder and on the role played in their definition by tests for internal chattering.

The expressive power of unique total stable model semantics
by Francesco Buccafurri, Sergio Greco, Domenico Sacca

Total stable (T-stable) models give a simple, yet powerful semantics to logic programming with negation. A peculiarity of T-stable models is their multiplicity and whether this is an advantage or a disadvantage is matter of long discussions. In this paper we show what is the precise expressive power of T-stable models when uniqueness is required, i.e., a query give an answer if and only if there exists a unique T-stable model. Our main result is that DATALOG queries with unique T-stable model semantics is able to express exactly all decision problems with unique solutions. Next, we analize the expressive powers of subclasses of DATALOG queries for which there exists at most one T-stable model. A surprising result is that any practical language for such queries has the same power as DATALOG with stratified negation.

Monadic simultaneous rigid E-unification and related problems.
by Yuri Gurevich, Andrei Voronkov

We study the monadic case of a decision problem know as simultaneous rigid E-unification. We show its equivalence to an extension of word equations. We prove decidability and complexity results for special cases of this problem.

Labelled Reductions, Runtime Errors, and Operational Subsumption
by Laurent DAMI

We propose a general framework for the operational semantics of errors. Errors are represented explicitly by a specific constant \err and reduction rules are completed in such a way that all ``wrong'' or ``stuck'' terms reduce to \err. As any other value, \err\ can be passed around, sometimes in a lazy way, and therefore an error occurring inside a term is not necessarily propagated to the top level; a term is considered ``erroneous'' if and only if it always generates \err. However, we require that errors are ``absorbing'', i.e. any attempt to interact with an error yields an error again (there is no way to recover from an error). Because of these requirements, \err\ naturally becomes the TOP element in the semantics. Hence \err\ has a special status, distinct from other, usual constants, and also distinct from divergence. There are many advantages to this approach:
- the resulting semantic structure is a lattice, which is much simpler that the various forms of cpo models which are currently prevalent in semantics, and comes back to the original structures of Scott.
- by comparing terms on their error-generation behaviour, we define an operational ordering called SUBSUMPTION which gives a precise meaning to the notion of ``substitutability'' or ``safe replacement'' often used informally in the object-oriented literature.
- we build a type system including a type \top which CONTAINS the error element}. This allows us to type more terms: unification of some type variables with \top yields valid typings for some programs that would be rejected by most other type systems.
For the technical development below we make heavy use LABELLED REDUCTIONS, an old idea used in the lambda-calculus to restrict the interaction behaviour of a term to a finite number of steps. Here this is generalised in an abstract way to other reduction systems. Labelled reductions allow us to classify both terms and contexts according to the number of interaction steps they can perform, and therefore introduce an operational notion of finite approximation. This in turn can be used as an alternative to the embedding-projection pairs of domain theory for solving recursive type equations.

A proof theoretical approach to communication
by Yuxi Fu

The paper investigates a concurrent computation model in which communications resemble cut eliminations for classical proofs. The algebraic properties of the model are studied. Its relationship to sequential computations is illustrated by showing that it incorporates the operational semantics of the call-by-name \lambda-calculus. Practically the model has \pi-calculus as a submodel.

Computability on the Probability Measures on the Borel Sets of the Unit Interval
by Klaus Weihrauch

Not avalaible