Undecidability of bisimilarity for Petri nets and some related problems

Jancar, Petr

doi:10.1016/0304-3975(95)00037-w

Cited by 109 publications

(94 citation statements)

References 13 publications

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“…Exploiting the encoding, we immediately obtain that these bisimilarities are undecidable also for open nets. This fact falls outside the known undecidability of bisimilarity for Petri nets [29], as we only observe the interaction with the environment: internal transitions are indistinguishable for strong equivalences and unobservable for weak equivalences (e.g., all standard, closed Petri nets are weakly bisimilar in our setting). In the other direction, using the fact that reachability is decidable for Petri nets, through the encoding we prove that reachability and convergence are decidable for bound asynchronous CCS (which, thus, is not Turing powerful).…”

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confidence: 75%

Encoding Asynchronous Interactions Using Open Petri Nets

Baldan

Bonchi

Gadducci

2009

CONCUR 2009 - Concurrency Theory

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Abstract. We present an encoding for (bound) processes of the asynchronous CCS with replication into open Petri nets: ordinary Petri nets equipped with a distinguished set of open places. The standard token game of nets models the reduction semantics of the calculus; the exchange of tokens on open places models the interactions between processes and their environment. The encoding preserves strong and weak CCS asynchronous bisimilarities: it thus represents a relevant step in establishing a precise correspondence between asynchronous calculi and (open) Petri nets. The work is intended as fostering the technology transfer between these formalisms: as an example, we discuss how some results on expressiveness can be transferred from the calculus to nets and back.

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confidence: 75%

Encoding Asynchronous Interactions Using Open Petri Nets

Baldan

Bonchi

Gadducci

2009

CONCUR 2009 - Concurrency Theory

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“…Let us examine three well-known equivalences over finite P/T nets: interleaving bisimilarity (Definition 7), step bisimilarity [27] and net isomorphism (Definition 5). On the one hand, only net isomorphism is decidable for finite P/T nets, while interleaving bisimilarity and step bisimilarity are undecidable [12,21]. On the other hand, net isomorphism is not a congruence for +: for instance, p = a.…”

Section: Resultsmentioning

confidence: 99%

Language representability of finite place/transition Petri nets

Gorrieri

2015

Vietnam J Comput Sci

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Finite-net multi-CCS is a CCS-like calculus which is able to model atomic sequences of actions and, together with parallel composition, also multi-party synchronization. This calculus is equipped with a labeled transition system semantics and also with an unsafe P/T Petri net semantics, which is sound w.r.t. the transition system semantics. For any process p of the calculus, the net associated to p by the semantics has always a finite number of places, but it has a finite number of transitions only for so-called well-formed processes. The main result of the paper is that well-formed finite-net multi-CCS processes are able to represent all finite, statically reduced, P/T Petri nets.

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“…One way to put it is to say that all interesting relations between lossy counter machines are undecidable, even if we only consider lossy VAS's (i.e., lossy counter machines without zero-tests). A proof for all relations between bisimilarity and trace containment can be obtained (see [42]) by adapting Jančar's classic proof for Petri nets [30]. The proof certainly extends, e.g., to all equivalences between equality of the reachability set and trace containment modulo invisibility of internal steps.…”

Section: Equivalence Checkingmentioning

confidence: 99%

Lossy Counter Machines Decidability Cheat Sheet

Schnoebelen

2010

Lecture Notes in Computer Science

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Abstract. Lossy counter machines (LCM's) are a variant of Minsky counter machines based on weak (or unreliable) counters in the sense that they can decrease nondeterministically and without notification. This model, introduced by R. Mayr [TCS 297:337-354 (2003)], is not yet very well known, even though it has already proven useful for establishing hardness results. In this paper we survey the basic theory of LCM's and their verification problems, with a focus on the decidability/undecidability divide.

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Undecidability of bisimilarity for Petri nets and some related problems

Cited by 109 publications

References 13 publications

Encoding Asynchronous Interactions Using Open Petri Nets

Encoding Asynchronous Interactions Using Open Petri Nets

Language representability of finite place/transition Petri nets

Lossy Counter Machines Decidability Cheat Sheet

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