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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 68 (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
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 45 (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...
Uniformization of Rational Relations
"... Uniformizing a relations belonging to some family, consists of finding... ..."
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Cited by 2 (2 self)
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Uniformizing a relations belonging to some family, consists of finding...
A Survey of Arithmetical Definability
, 2002
"... We survey definability and decidability issues related to firstorder fragments of arithmetic, with a special emphasis on Presburger and Skolem arithmetic and their (un)decidable extensions. ..."
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Cited by 2 (0 self)
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We survey definability and decidability issues related to firstorder fragments of arithmetic, with a special emphasis on Presburger and Skolem arithmetic and their (un)decidable extensions.
On the ContextFreeness Problem for Vector Addition Systems
, 2013
"... Abstract—Petri nets, or equivalently vector addition systems (VAS), are widely recognized as a central model for concurrent systems. Many interesting properties are decidable for this class, such as boundedness, reachability, regularity, as well as contextfreeness, which is the focus of this paper. ..."
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Cited by 1 (1 self)
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Abstract—Petri nets, or equivalently vector addition systems (VAS), are widely recognized as a central model for concurrent systems. Many interesting properties are decidable for this class, such as boundedness, reachability, regularity, as well as contextfreeness, which is the focus of this paper. The contextfreeness problem asks whether the trace language of a given VAS is contextfree. This problem was shown to be decidable by Schwer in 1992, but the proof is very complex and intricate. The resulting decision procedure relies on five technical conditions over a customized coverability graph. These five conditions are shown to be necessary, but the proof that they are sufficient is only sketched. In this paper, we revisit the contextfreeness problem for VAS, and give a simpler proof of decidability. Our approach is based on witnesses of noncontextfreeness, that are bounded regular languages satisfying a nesting condition. As a corollary, we obtain that the trace language of a VAS is contextfree if, and only if, it has a contextfree intersection with every bounded regular language. KeywordsVector addition systems, Petri nets, contextfreeness, pushdown automata, bounded languages, semilinear sets. I.
On some counting problems for semilinear sets ∗
, 907
"... Stefano Varricchio suddenly passed away on August 20th 2008, shortly after this paper has been completed. We will remember Stefano as the best friend of us and as an outstanding researcher. Working with Stefano was always an enthusiastic experience both for his beautiful and original ideas and for h ..."
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Stefano Varricchio suddenly passed away on August 20th 2008, shortly after this paper has been completed. We will remember Stefano as the best friend of us and as an outstanding researcher. Working with Stefano was always an enthusiastic experience both for his beautiful and original ideas and for his scientific rigueur. Let X be a subset of N t or Z t. We can associate with X a function GX: N t − → N which returns, for every (n1,..., nt) ∈ N t, the number GX(n1,..., nt) of all vectors x ∈ X such that, for every i = 1,..., t, xi  ≤ ni. This function is called the growth function of X. The main result of this paper is that the growth function of a semilinear set of N t or Z t is a box spline. By using this result and some theorems on semilinear sets, we give a new proof of combinatorial flavour of a wellknown theorem by
Available online at: www.rairoita.org AFFINE PARIKH AUTOMATA ∗
"... Abstract. The Parikh finite word automaton (PA) was introduced and studied in 2003 by Klaedtke and Rueß. Natural variants of the PA arise from viewing a PA equivalently as an automaton that keeps a count of its transitions and semilinearly constrains their numbers. Here we adopt this view and define ..."
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Abstract. The Parikh finite word automaton (PA) was introduced and studied in 2003 by Klaedtke and Rueß. Natural variants of the PA arise from viewing a PA equivalently as an automaton that keeps a count of its transitions and semilinearly constrains their numbers. Here we adopt this view and define the affine PA, that extends the PA by having each transition induce an affine transformation on the PA registers, and the PA on letters, that restricts the PA by forcing any two transitions on the same letter to affect the registers equally. Then we report on the expressiveness, closure, and decidability properties of such PA variants. We note that deterministic PA are strictly weaker than deterministic reversalbounded counter machines. Mathematics Subject Classification. 68Q45. 1.
Acceleration For Presburger Petri Nets
"... The reachability problem for Petri nets is a central problem of net theory. The problem is known to be decidable by inductive invariants definable in the Presburger arithmetic. When the reachability set is definable in the Presburger arithmetic, the existence of such an inductive invariant is immedi ..."
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The reachability problem for Petri nets is a central problem of net theory. The problem is known to be decidable by inductive invariants definable in the Presburger arithmetic. When the reachability set is definable in the Presburger arithmetic, the existence of such an inductive invariant is immediate. However, in this case, the computation of a Presburger formula denoting the reachability set is an open problem. Recently this problem got closed by proving that if the reachability set of a Petri net is definable in the Presburger arithmetic, then the Petri net is flatable, i.e. its reachability set can be obtained by runs labeled by words in a bounded language. As a direct consequence, classical algorithms based on acceleration techniques effectively compute a formula in the Presburger arithmetic denoting the reachability set. 1