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26
Recognizing string graphs in NP
 J. of Computer and System Sciences
"... A string graph is the intersection graph of a set of curves in the plane. Each curve is represented by a vertex, and an edge between two vertices means that the corresponding curves intersect. We show that string graphs can be recognized in NP. The recognition problem was not known to be decidable u ..."
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Cited by 25 (4 self)
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A string graph is the intersection graph of a set of curves in the plane. Each curve is represented by a vertex, and an edge between two vertices means that the corresponding curves intersect. We show that string graphs can be recognized in NP. The recognition problem was not known to be decidable until very recently, when two independent papers established exponential upper bounds on the number of intersections needed to realize a string graph (Pach and Tóth, 2001; Schaefer and ˇ Stefankovič, 2001). These results implied that the recognition problem lies in NEXP. In the present paper we improve this by showing that the recognition problem for string graphs is in NP, and therefore NPcomplete, since Kratochvíl showed that the recognition problem is NPhard (Kratochvíl, 1991b). The result has consequences for the computational complexity of problems in graph drawing, and topological inference. We also show that the string graph problem is decidable for surfaces of arbitrary genus. Key words: String graphs, NPcompleteness, graph drawing, topological inference, Euler diagrams
Planning as Satisfiability: Parallel Plans and Algorithms for Plan Search
 ARTIF. INTELL
, 2005
"... ..."
Bounded Reachability Checking with Process Semantics
 In Proceedings of the 12th International Conference on Concurrency Theory (Concur’2001
, 2001
"... Bounded model checking has been recently introduced as an efficient verification method for reactive systems. In this work we apply bounded model checking to asynchronous systems. More specifically, we translate the bounded reachability problem for 1safe Petri nets into constrained Boolean circuit ..."
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Cited by 20 (5 self)
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Bounded model checking has been recently introduced as an efficient verification method for reactive systems. In this work we apply bounded model checking to asynchronous systems. More specifically, we translate the bounded reachability problem for 1safe Petri nets into constrained Boolean circuit satisfiability. We consider three semantics: process, step, and interleaving semantics. We show that process semantics has often the best performance for bounded reachability checking.
Divisibility Theory and Complexity of Algorithms for Free Partially Commutative
 Groups, Contemp. Math. 378 (Groups, Languages, Algorithms
, 2005
"... Nota Bene. The original version of the paper was published ..."
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Cited by 13 (7 self)
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Nota Bene. The original version of the paper was published
Generalised Regular MSC Languages
 PROCEEDINGS OF THE 5TH INTERNATIONAL CONFERENCE ON FOUNDATIONS OF SOFTWARE SCIENCE AND COMPUTATION STRUCTURES (FOSSACS’02), LECTURE NOTES IN COMPUTER SCIENCE 2303, SPRINGERVERLAG
, 2002
"... In this paper, we establish the concept of regularity for languages consisting of Message Sequence Charts (MSCs). To this aim, we formalise their behaviour by string languages and give a natural definition of regularity in terms of an appropriate Nerode right congruence. Moreover, we present a class ..."
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Cited by 6 (3 self)
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In this paper, we establish the concept of regularity for languages consisting of Message Sequence Charts (MSCs). To this aim, we formalise their behaviour by string languages and give a natural definition of regularity in terms of an appropriate Nerode right congruence. Moreover, we present a class of accepting automata and, using this characterisation, establish several decidability and closure properties of MSC languages. We also provide a logical characterisation by a monadic secondorder logic interpreted over MSCs. In contrast to existing work on regular MSC languages, our approach is neither restricted to a certain class of MSCs nor tailored to a fixed communication medium (such as a FIFO channel). It explicitly allows MSCs with message overtaking and is thus applicable to a broad range of channel types like mixtures of stacks and FIFOs.
On the average parallelism in trace monoids
 Proceedings of STACS’02, LNCS
, 2002
"... The height of a trace is the height of the corresponding heap of pieces in Viennot’s representation, or equivalently the number of factors in its CartierFoata decomposition. Let h(t) and t  stand respectively for the height and the length of a trace t. We prove that the bivariate commutative seri ..."
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Cited by 6 (1 self)
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The height of a trace is the height of the corresponding heap of pieces in Viennot’s representation, or equivalently the number of factors in its CartierFoata decomposition. Let h(t) and t  stand respectively for the height and the length of a trace t. We prove that the bivariate commutative series ∑ t xh(t) y t  is rational, and we give a finite representation of it. We use the rationality to obtain precise information on the asymptotics of the number of traces of a given height or length. Then, we study the average height of a trace for various probability distributions on traces. For the uniform probability distribution on traces of the same length (resp. of the same height), the asymptotic average height (resp. length) exists and is an algebraic number. To illustrate our results and methods, we consider a couple of examples: the free commutative monoid and the trace monoid whose independence graph is the ladder graph.
BMC via OntheFly Determinization
, 2003
"... The paper develops novel bounded model checking techniques for labelled transition systems. The aim is to increase the e#ciency of BMC by exploiting the inherent concurrency in the product of LTSs in order to cover more executions of the product within a given bound. This is done by considering a no ..."
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Cited by 6 (1 self)
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The paper develops novel bounded model checking techniques for labelled transition systems. The aim is to increase the e#ciency of BMC by exploiting the inherent concurrency in the product of LTSs in order to cover more executions of the product within a given bound. This is done by considering a nonstandard execution model, step executions, where multiple actions can take place simultaneously and where component LTSs are determinized onthefly, i.e., a component may be in a set of states in a step instead of in just one as in standard interleaving executions. Step executions can be further restricted to a subclass called process executions without loosing reachable states. For bounded model checking of reachability properties of the product of LTSs the paper presents translation schemes from LTSs to a constrained Boolean circuit such that satisfying valuations of the circuit correspond to step (process) executions of the product. The translation schemes have been implemented and some experimental comparisons performed. The results show that the bound needed for step and process executions is in most cases lower than in interleaving executions and that the running time of the model checker using process executions is smaller than using steps. Moreover, the performance compares favorably to a stateoftheart interleaving BMC implementation in the NuSMV system.
The Topology of Mazurkiewicz Traces
"... The present paper characterizes the topological structure of real traces. This is done in terms of graphtheoretic properties of the underlying dependence alphabet, which may be innite. The topological space of real traces is shown to be homeomorphic to the direct product of (at most) the full b ..."
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Cited by 5 (0 self)
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The present paper characterizes the topological structure of real traces. This is done in terms of graphtheoretic properties of the underlying dependence alphabet, which may be innite. The topological space of real traces is shown to be homeomorphic to the direct product of (at most) the full binary tree and the full countably branching tree and one higherdimensional grid. The occurrence of each of these factors depends on the existence of nite nontrivial and of innite connected components and on the number of isolated letters of the dependence alphabet. 1 Introduction Trace monoids were introduced by Cartier and Foata [3], who investigated combinatorial problems concerning the rearrangement of words, and by Mazurkiewicz [14], who was motivated to provide a mathematical model for concurrent systems. Since then trace theory has become a very popular topic, see the recent surveys [5, 6]. Corresponding author. This work was written while the second author worked at th...
Random Generation and Approximate Counting of Ambiguously Described Combinatorial Structures
 Proceedings of 17th Annual Symposium on Theoretical Aspects of Computer Science (STACS), number 1770 in Lecture Notes in Computer Science
, 2000
"... This paper concerns the uniform random generation and the approximate counting of combinatorial structures admitting an ambiguous description. We propose a general framework to study the complexity of these problems and present some applications to specic classes of languages. In particular, we ..."
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Cited by 4 (1 self)
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This paper concerns the uniform random generation and the approximate counting of combinatorial structures admitting an ambiguous description. We propose a general framework to study the complexity of these problems and present some applications to specic classes of languages. In particular, we give a uniform random generation algorithm for nitely ambiguous contextfree languages of the same time complexity of the best known algorithm for the unambiguous case. Other applications include a polynomial time uniform random generator and approximation scheme for the census function of (i) languages recognized in polynomial time by oneway nondeterministic auxiliary pushdown automata of polynomial ambiguity and (ii) polynomially ambiguous rational trace languages. Keywords: uniform random generation, approximate counting, contextfree languages, auxiliary pushdown automata, rational trace languages, inherent ambiguity. 1 Introduction In this work we propose a general framewo...