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69
Logic and precognizable sets of integers
 Bull. Belg. Math. Soc
, 1994
"... We survey the properties of sets of integers recognizable by automata when they are written in pary expansions. We focus on Cobham’s theorem which characterizes the sets recognizable in different bases p and on its generalization to N m due to Semenov. We detail the remarkable proof recently given ..."
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Cited by 88 (4 self)
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We survey the properties of sets of integers recognizable by automata when they are written in pary expansions. We focus on Cobham’s theorem which characterizes the sets recognizable in different bases p and on its generalization to N m due to Semenov. We detail the remarkable proof recently given by Muchnik for the theorem of CobhamSemenov, the original proof being published in Russian. 1
Petri Nets, Commutative ContextFree Grammars, and Basic Parallel Processes
, 1997
"... . The paper provides a structural characterisation of the reachable markings of Petri nets in which every transition has exactly one input place. As a corollary, the reachability problem for this class is proved to be NPcomplete. Further consequences are: the uniform word problem for commutative co ..."
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Cited by 68 (6 self)
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. The paper provides a structural characterisation of the reachable markings of Petri nets in which every transition has exactly one input place. As a corollary, the reachability problem for this class is proved to be NPcomplete. Further consequences are: the uniform word problem for commutative contextfree grammars is NPcomplete; weakbisimilarity is semidecidable for Basic Parallel Processes. Keywords: Petri nets, Commutative Contextfree Grammars, Basic Parallel Processes, Weak bisimilarity. 1. Introduction The reachability problem plays a central role in Petri net theory, and has been studied in numerous papers (see [5] for a comprehensive list of references). In the first part of this paper we study it for the nets in which every transition needs exactly one token to occur. Following [8], we call them communicationfree nets, because no cooperation between places is needed in order to fire a transition; every transition is activated by one single token, and the tokens may flow...
Undecidability of Bisimilarity for Petri Nets and Some Related Problems
, 1995
"... The main result shows the undecidability of (strong) bisimilarity for labelled (place / transition) Petri nets. The technique of the proof applies to the language (or trace) equivalence and the reachability set equality as well, which yields stronger versions with simpler proofs of already known ..."
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Cited by 59 (3 self)
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The main result shows the undecidability of (strong) bisimilarity for labelled (place / transition) Petri nets. The technique of the proof applies to the language (or trace) equivalence and the reachability set equality as well, which yields stronger versions with simpler proofs of already known results. The paper also contains two decidability results. One concerns the Petri nets which are deterministic up to bisimilarity, the other concerns semilinear bisimulations and extends the result of [4] for Basic Parallel Processes. 1 Introduction The topic of the paper belongs to an interesting area in the theory of parallelism and concurrency, namely to the area of decidability questions for behavioural equivalences in various classes of (models of) processes. These questions are among the rst ones to ask when developing automated verication methods, for example. There is a large amount of equivalences in the literature (cf. e.g. [9]), nevertheless some of them are felt to be mor...
Reachability in Petri Nets with Inhibitor arcs
, 2004
"... We define 2 operators on relations over natural numbers such that they generalize the operators '+' and '*' and show that the membership and emptiness problem of relations constructed from finite relations with these operators and is decidable. This generalizes Presburger arith ..."
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Cited by 28 (0 self)
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We define 2 operators on relations over natural numbers such that they generalize the operators '+' and '*' and show that the membership and emptiness problem of relations constructed from finite relations with these operators and is decidable. This generalizes Presburger arithmetics and allows to decide the reachability problem for those Petri nets where inhibitor arcs occur only in some restricted way. Especially the reachability problem is decidable for Petri nets with only one inhibitor arc, which solves an open problem in [KLM89] . Furthermore we describe the corresponding automaton having a decidable emptiness problem. 1
Flat Counter Automata Almost Everywhere
 In ATVA ’05
"... Abstract. This paper argues that flatness appears as a central notion in the verification of counter automata. A counter automaton is called flat when its control graph can be “replaced”, equivalently w.r.t. reachability, by another one with no nested loops. From a practical view point, we show that ..."
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Cited by 25 (6 self)
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Abstract. This paper argues that flatness appears as a central notion in the verification of counter automata. A counter automaton is called flat when its control graph can be “replaced”, equivalently w.r.t. reachability, by another one with no nested loops. From a practical view point, we show that flatness is a necessary and sufficient condition for termination of accelerated symbolic model checking, a generic semialgorithmic technique implemented in successful tools like FAST, LASH or TREX. From a theoretical view point, we prove that many known semilinear subclasses of counter automata are flat: reversal bounded counter machines, lossy vector addition systems with states, reversible Petri nets, persistent and conflictfree Petri nets, etc. Hence, for these subclasses, the semilinear reachability set can be computed using a uniform accelerated symbolic procedure (whereas previous algorithms were specifically designed for each subclass). 1
Remarks on piecewiselinear algebra
 Paci J. Math
, 1982
"... This note studies some of the basic properties of the category whose objects are finite unions of (open and closed) polyhedra and whose morphisms are (not necessarily continuous) piecewiselinear maps. Introduction * A function f: V —>W between real vector spaces is piecewiselinear (PL) if ther ..."
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Cited by 25 (5 self)
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This note studies some of the basic properties of the category whose objects are finite unions of (open and closed) polyhedra and whose morphisms are (not necessarily continuous) piecewiselinear maps. Introduction * A function f: V —>W between real vector spaces is piecewiselinear (PL) if there exists a partition of V into "open polyhedra " X (i.e., relative interiors of polyhedra) such that / is
Some Complexity Results for Polynomial Ideals
, 1997
"... In this paper, we survey some of our new results on the complexity of a number of problems related to polynomial ideals. We consider multivariate polynomials over some ring, like the integers or the rationals. For instance, a polynomial ideal membership problem is a (w + 1)tuple P = ( f, g1, g2,.. ..."
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Cited by 21 (0 self)
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In this paper, we survey some of our new results on the complexity of a number of problems related to polynomial ideals. We consider multivariate polynomials over some ring, like the integers or the rationals. For instance, a polynomial ideal membership problem is a (w + 1)tuple P = ( f, g1, g2,..., gw) where f and the gi are multivariate polynomials, and the problem is to determine whether f is in the ideal generated by the gi. For polynomials over the integers or rationals, this problem is known to be exponential space complete. We discuss further complexity results for problems related to polynomial ideals, like the word and subword problems for commutative semigroups, a quantitative version of Hilbert’s Nullstellensatz in a complexity theoretic version, and problems concerning the computation of reduced polynomials and Gröbner bases.
A Superexponential Lower Bound for Gröbner Bases and ChurchRosser Commutative Thue Systems
, 1986
"... The complexity of the normal form algorithms which transform a given polynomial ideal basis into a Gröbner basis or a given commutative Thue system into a ChurchRosser system is presently unknown. In this paper we derive a doubleexponential lower bound (22") for the production length and card ..."
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Cited by 21 (0 self)
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The complexity of the normal form algorithms which transform a given polynomial ideal basis into a Gröbner basis or a given commutative Thue system into a ChurchRosser system is presently unknown. In this paper we derive a doubleexponential lower bound (22") for the production length and cardinality of ChurchRosser commutative Thue systems, and the degree and cardinality of Gröbner bases.
Rational Series over Dioids and Discrete Event Systems
 In Proc. of the 11th Conf. on Anal. and Opt. of Systems: Discrete Event Systems, number 199 in Lect. Notes. in Control and Inf. Sci, Sophia Antipolis
, 1994
"... this paper is obviously too short for such a program, we have chosen to propose an introductive guided tour. A more detailed exposition will be found in our references and in a more complete paper to appear elsewhere. 1 Rational Series in a Single Indeterminate ..."
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Cited by 18 (7 self)
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this paper is obviously too short for such a program, we have chosen to propose an introductive guided tour. A more detailed exposition will be found in our references and in a more complete paper to appear elsewhere. 1 Rational Series in a Single Indeterminate