Jancar, P: "Undecidability of Bisimilarity for Petri Nets and Some Related Problems", Theoretical Computer Science 148, 1995, 281--301.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....applicability. Last but not least, many problems about the composition and the behavioural subtyping of Petri nets are decidable when the language of the net is regular. This property is noteworthy, since most of equivalence preorder (equivalence) relations are undecidable for labelled Petri nets [10]. In [7] we show that it is decidable whether: a language of a Petri net is regular, a component is (strongly and or weakly) compatible with (resp. transparent for) an agent component. These results are proved using a construction due to Vogler [20] The approach presented in this paper, leads ....

P. Jancar. Undecidability of Bisimilarity for Petri Nets and some related problems. Theoretical Computer Science, N 148, 1995.

....least, many problems about the composition and the behavioural subtyping of Petri nets are decidable when the language of the nets is regular even if they are unbounded. This property is noteworthy, since most of equivalence preorder (equivalence) relations are undecidable for labelled Petri nets [Jancar 95] In [Hameurlain 98] we have shown that it is decidable whether: a language of a Petri net is regular, a server net is (strongly and or weakly) compatible (resp. transparent for) with a client net, and two regular nets are language equivalent. We prove that the language equivalence between two ....

P. Jancar. Undecidability of Bisimilarity for Petri Nets and some related problems. Theoretical Computer Science, N 148, 1995.

....silent action , which plays a similar role to moves in finite automata. The firing of these transitions is assumed to be unobservable. Unfortunately, already the strong versions (along with the strong versions of all reasonable behavioural equivalences) are undecidable for general Petri nets [10, 11, 12], in fact even for Petri nets having at most two unbounded places. Faced with such a negative result, a natural step then is to restrict the problem in some way. For example, for the class of Petri nets in which every transition has a single input place the so called Basic Parallel ....

....the trace set in the case where the transitions are uniquely labelled. To demonstrate this result, we rely on the undecidability of the halting problem for Minsky counter machines. To a counter machine C (zero input values are supposed) we construct a net NC with initial marking M 0 (inspired by [10] as modified in [6] for which we can demonstrate the following: 1. If the counter machine C halts, then M 0 is trace equivalent to some finite state process r; 2. If the machine C does not halt, then M 0 is not trace equivalent to any finite state process r. Remark: The above mentioned ....

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P. Jancar, Undecidability of bisimilarity for Petri nets and some related problems. Theor. Comput. Sci. 148 (1995), 281--301.

....grammars. This was extended to all BPA processes and then to pushdown automata [5, 16, 14] Decidability of bisimilarity was also shown for Basic Parallel (BP) processes, a restricted subset of Petri nets, 4] For full Petri nets Jancar proved that bisimulation equivalence is undecidable [11]. An open question is the dividing line between decidability and undecidability of bisimilarity in the case of sequential systems. For instance, is bisimulation equivalence decidable for the general class of prefix recognisable transition graphs introduced by Caucal [2] A poignant problem is ....

Jancar, P. (1995). Undecidability of bisimilarity for Petri nets and some related problems. Theoretical Computer Science, 148, 281-301.

.... hard [108] exptime [87] pspace hard [108] pspace hard [108] BPP decidable [36] co np hard [107] ptime in the normed case [71] pspace [87] decidable [55] co np hard [107] PA co np hard [107] decidable in the normed case [68] decidable [87] co np hard [107] PN undecidable [85] decidable [55] EXpspace hard [108] decidable [55] expspace hard [108] Figure 2: Results for bisimilarity. 2.5 Summary of Results The tables in Figures 2 and 3 summarise a variety of decidability and algorithmic results for bisimulation problems over several classes of infinite state ....

.... FSA regularity BPA pspace hard [139] ptime [99] PDA pspace hard [139] exptime [87] pspace hard [108] pspace hard [108] BPP np hard [139] Pi P 2 hard [107] pspace [87] Pi P 2 hard [107] PA pspace hard [139] decidable [87] Pi P 2 hard [107] PN undecidable [85] undecidable [55] undecidable [55] Figure 3: Results for weak bisimilarity. the sense that we omit the second clause in Definition 9, and in the third clause we only demand that fi be a final state whenever ff is, but not vice versa. We then say that ff is simulated by fi if the pair (ff; fi) is ....

P. Jancar. Undecidability of bisimilarity for Petri nets and some related problems. Theoretical Computer Science, 148:281--301, 1995.

....of these equivalences for systems with infinite state spaces started to receive a lot of attention, and led to renewed interest in Petri nets. Jancar proved only a few years ago a fundamental result showing the undecidability for Petri nets of all equivalence notions described in the literature [22, 21]. These two developments still had another effect. During the eighties, many researchers started to study the relationship of process algebras to Petri nets. Net models in which a place can carry at most one token, like condition event systems or elementary net systems, turned out to be ....

....equivalence problems for Petri nets are undecidable. This rule is supported by a recent and very nice result due to Jancar, showing that every equivalence notion between trace and bisimulation equivalence is undecidable for Petri nets. 13 Jancar himself has presented his result very clearly in [22]; here we do it in a slightly different way. We proceed by reduction from the problem 13 Actually, the result is a bit stronger, since bisimulation can be replaced by an even finer equivalence. Given: a counter program C, To decide: if C halts (recall that all counters are initialised to 0) ....

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P. Jancar. Undecidability of Bisimilarity for Petri Nets and Some Related Problems. Theoretical Computer Science, 148:281--301, 1995.

.... first one is an open question of decidability of bisimulation equivalence for fcBPP since the decidability of bisimulation equivalence for BPP has been already proven by Christensen, Hirshfeld and Moller [CHM93] Using Jancar s method for proving undecidability of bisimulation equivalence for PN ([Jan95]) Moller [Mol96] has shown that bisimulation equivalence 27 is undecidable for PPDA. The second interesting challenge is to specify the boundary of decidability of weak bisimulation equivalence with finite state processes. Mayr has proved in [May96] that weak bisimulation equivalence with ....

P. Jancar. Undecidability of bisimilarity for Petri nets and some related problems. Theoretical Computer Science, 148(2):281--301, 1995.

....the class of context free languages. This argument can be shown to hold for the class of normed BPA systems as well. This undecidability result extends also to all equivalences which lie in 16 Glabbeek s spectrum [vG90b] between bisimilarity and language equivalence [GH94, HT95] Another result [Jan95] due to Jancar says that bisimilarity is undecidable for Petri Nets. We generalise the approach of Bosscher [Bos97] and show that the decidability of (strict and nonstrict) bisimilarity in BPA systems extends to BPA # systems. In the proof we exploit the result in [CHS92] and transform the ....

P. Jancar. Undecidability of bisimilarity for Petri nets and some related problems. Theoretical Computer Science, 148(2):281--301, 1995.

....the class of context free languages. This argument can be shown to hold for the class of normed BPA systems as well. This undecidability result extends also to all equivalences which lie in Glabbeek s spectrum [vG90b] between bisimilarity and language equivalence [GH94, HT95] Another result [Jan95] due to Jancar says that bisimilarity is undecidable for Petri Nets. We show that the decidability of bisimilarity in BPA systems can be extended to BPA ffi systems. In the proof we exploit the result in [CHS92] and transform the examined BPA ffi systems into BPA systems, interpreting ffi as a ....

P. Jancar. Undecidability of bisimilarity for Petri nets and some related problems. Theoretical Computer Science, 148(2):281--301, 1995.

....infinite state systems. In this paper, we finally settle the question of decidability of hhp bisimilarity by showing it to be undecidable for finite 1 safe Petri nets. Similarly to according to our best knowledge the only other non trivial undecidability result for bisimilarity due to Jancar [Jan95], we reduce the halting problem for counter machines. Our technique is however quite di#erent, since Jancar considers the class of infinite state Petri nets, while finite 1 safe Petri nets are finite state. Jancar encodes configurations of a counting machine just as markings of an (infinite state) ....

Petr Jancar. Undecidability of bisimilarity for Petri nets and some related problems. Theoretical Computer Science, 148(2):281--301, 1995. 11

....general, even when A = N P . The proof is long, technical and is omitted. Basically, it shows that the problem of telling whether two places p and q are such that Id [ f(p; q) q; p)g is a correct fusion for N;N P is undecidable. This reuses ideas from [Qui95] extending Jancar s technique [Jan95] to a setting where all possible markings may be considered. 8 Place bisimulation Since R(N;A) cannot be computed in general, we settle for a computable approximation: place bisimulation. In the following we assume a net N and a succ closed set A of relevant markings are fixed. The following ....

P. Jancar. Undecidability of bisimilarity for Petri nets and some related problems. Theoretical Computer Science, 148(2):281--301, 1995.

....been studied intensively (see [26] for a survey) While many algorithms for bisimulation problems have a very high complexity, only few lower bounds are known. The state of the art. Strong bisimilarity of two Petri nets and weak bisimilarity of a Petri net and a finite automaton is undecidable [13, 14]. Weak bisimilarity for Basic Parallel Processes (BPP) is NP hard and weak bisimilarity for context free processes (BPA) is PSPACE hard [31] However, it is still an open question whether these problems are decidable. Some lower bounds for decidable bisimulation problems have been shown in [23] ....

....fragment of CCS [25] without communication, restriction and relabeling. They are equivalent to communication free nets [8] the subclass of Petri nets [28] where every transition has exactly one input place with arc weight one. While strong (and weak) bisimilarity are undecidable for Petri nets [13], strong bisimilarity is decidable for BPP (i.e. communication free nets) 7] However, the algorithm in [7] has non elementary complexity and, to the best of our knowledge, no better algorithm has been found since then. In spite of this, no lower bound for the problem has been found either. ....

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P. Jancar. Undecidability of bisimilarity for Petri nets and some related problems. Theoretical Computer Science, 148:281--301, 1995.

....in the theory of process algebras [21] The decidability and complexity of bisimulation problems for infinite state systems has been studied intensively (see [22] for a survey) While many algorithms for bisimulation problems have a very high complexity, only few lower bounds are known. Jancar [12, 13] showed that strong bisimilarity of two Petri nets [25] and weak bisimilarity of a Petri net and a finite automaton is undecidable. Str ibrn a [28] showed that weak bisimilarity for Basic Parallel Processes (BPP) is NP hard and weak bisimilarity for context free processes (BPA) is PSPACE hard. ....

.... [14] decidable [7] co NP hard [19] 2 PSPACE [14] NP hard [28] Pi p 2 hard [19] PA decidable [14] co NP hard [19] decidable [14] PSPACE hard [28] PAD decidable [14] PSPACE hard PSPACE hard decidable [14] PSPACE hard PSPACE hard [28] PN decidable [15, 14] EXPSPACE hard undecidable [12] undecidable [12] undecidable [12] PAN EXPSPACE hard undecidable [12] undecidable [12] undecidable [12] PRS EXPSPACE hard undecidable [12] undecidable [12] undecidable [12] 13 The following table summarizes results about the problems of strong and weak finiteness. New results are in boldface. ....

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P. Jancar. Undecidability of bisimilarity for Petri nets and some related problems. Theoretical Computer Science, 148:281--301, 1995.

....lies between these two extremes. However, the result is not optimal since not one relation between trace equivalence and bisimilarity is known to be in PSPACE for non flat systems. Indeed, Rab97a] conjectures that all these equivalences are EXPTIME hard. 1 A similar approach appears in [Jan95] where a single construction shows undecidability, over P T nets, of all equivalences between trace equivalence and bisimilarity. equivalence failure equivalence equivalence 2 nested simulation possible futures completed trace bisimulation equivalence equivalence ready simulation ready ....

P. Jancar. Undecidability of bisimilarity for Petri nets and some related problems. Theoretical Computer Science, 148(2):281--301, 1995.

....sets of places of N 1 and N 2 . f can be extended to a bijection on markings in the obvious way. Question: Is it true that for every reachable marking M of N 1 , f(M) is a reachable marking of N 2 Rabin showed that this problem is undecidable by reduction of Hilbert s 10th problem. Later Jancar [13,14] gave a more direct proof by a reduction from the halting problem for counter machines. We sketch the reduction of the reachability set containment problem to the model checking problem. It is similar to the one in [11] but slightly simpler. We assume that the transitions in the Petri nets N 1 ; ....

P. Jancar. Undecidability of bisimilarity for Petri nets and some related problems. Theoretical Computer Science, 148:281--301, 1995.

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Jancar, P. Undecidability of bisimilarity for Petri nets and some related problems. Journal of Theoretical Computer Science 148, pp281--301, 1995.

....topic [19] Example classes of processes of particular interest in this study are pushdown automata, Petri nets, and the process algebra PA. Some milestones in the study, beginning with the decidability of bisimilarity over normed BPA [1] include the undecidability of bisimilarity over Petri nets [10]; the decidability of bisimilarity over normed PA [7] and the decidability of bisimilarity over the class of strict deterministic grammars (a particular formulation of deterministic pushdown automata) 23] This final result reinforces Senizergues solution [18] to the long standing equivalence ....

P. Jancar. Undecidability of bisimilarity for Petri nets and some related problems. Theoretical Computer Science 148(2):281--301, 1995.

....They can thus be seen as simple parallel programs. Christensen, Hirshfeld and Moller proved in [CHM93] that bisimilarity is decidable for BPP processes. Another positive result [Sti96] is due to Stirling it says that bisimilarity is decidable for normed PDA processes. Jancar demonstrated in [Jan95] that bisimilarity is undecidable for labelled Petri nets. However, if one of those nets is bounded (i.e. finitestate) bisimilarity becomes decidable (see [JM95] Abdulla and Kindahl proved in [AK95] that bisimilarity is decidable between lossy channel systems and finite state processes. In ....

P. Jancar. Undecidability of bisimilarity for Petri nets and some related problems. Theoretical Computer Science, 148(2):281--301, 1995.

....silent action , which plays a similar role to moves in finite automata. The firing of these transitions is assumed to be unobservable. Unfortunately, already the strong versions (along with the strong versions of all reasonable behavioural equivalences) are undecidable for general Petri nets [10, 11, 12], in fact even for Petri nets having at most two unbounded places. Faced with such a negative result, a natural step then is to restrict the problem in some way. For example, for the class of Petri nets in which every transition has a single input place the so called Basic Parallel ....

....set in the case where the transitions are uniquely labelled. 14 To demonstrate this result, we rely on the undecidability of the halting problem for Minsky counter machines. To a counter machine C (zero input values are supposed) we construct a net NC with initial marking M 0 (inspired by [10] as modified in [6] for which we can demonstrate the following: 1. If the counter machine C halts, then M 0 is trace equivalent to some finite state process r; 2. If the machine C does not halt, then M 0 is not trace equivalent to any finite state process r. Remark: The above mentioned extension ....

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P. Jancar, Undecidability of bisimilarity for Petri nets and some related problems. Theor. Comput. Sci. 148 (1995), 281--301.

....is undecidable. Decidability of bisimulation like equivalences has been intensively studied for various process classes (see e.g. Mol96] for a complete survey) The majority of the results are about the decidability of strong bisimilarity, e.g. BBK93, CHS95, CHM93, Sti96, CKK97, Kuc97, Jan95] Strong bisimilarity with finite state processes is known to be decidable for (labelled) Petri nets [JM95] PA and pushdown processes [JK97] Another positive result of this kind is presented in [May96] where it is shown that weak bisimilarity is decidable between BPP and finite state ....

.... Deltaff A A AU A A AK f XXX Xz ae ae Q Qs Phi Phi : Q Qk c oe Figure 3 always a StExt(BPP) net, we would be done. In fact, it is not the case but NM can be suitably transformed. The depicted subnets N 1 and N 2 (with all transitions labelled by ) can be constructed as in [Jan95] for showing undecidability of the reachability set equality problem) At most 5 places in N 1 and 5 places in N 2 can be unbounded then; it can be easily verified that each their transition has at most 1 unbounded place among its input places. The only difficulty are the transitions in the ....

P. Jancar. Undecidability of bisimilarity for Petri nets and some related problems. Theoretical Computer Science, 148(2):281--301, 1995.

....nets) the problem of weak bisimilarity with finitestate processes is undecidable. Decidability of bisimulation like equivalences has been intensively studied for various process classes (see [28] for a survey) The majority of the results are about the decidability of strong bisimilarity, e.g. [3,9,8,34,7,16,12]. Strong bisimilarity with finite state processes is known to be decidable for 2 (labeled) Petri nets [15] PA, and pushdown processes [14] Another positive result of this kind is presented in [22] where it is shown that weak bisimilarity is decidable between BPP and finite state processes. ....

.... of D s in each step (after adding 1 in the case of a decreasing step) Now we add a control state h and the basic transition (Z DkZ; q n ; h) Defining vec(E) as the 5 dimensional vector giving the numbers of (occurrences of) I 1 ; I 2 ; C; D; S in E, we can easily derive (similarly as in [12]) that the set f vec(E) j 9r such that (r; E) is reachable from (p 1 ; Z) g is a subset of f vec(E) j 9r such that (r; E) is reachable from (q 1 ; Z) g; moreover, the two sets are equal iff M does not halt. To proceed with the construction of our desired P (M) we now take a disjoint union of the ....

P. Jancar. Undecidability of bisimilarity for Petri nets and some related problems. Theoretical Computer Science, 148(2):281--301, 1995.

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Jancar, P: "Undecidability of Bisimilarity for Petri Nets and Some Related Problems", Theoretical Computer Science 148, 1995, 281--301.

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P. Jancar. Undecidability of Bisimilarity for Petri Nets and Some Related Problems. Theoretical Computer Science, 148:281--301, 1995.

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P. Jancar. Undecidability of bisimilarity for Petri nets and some related problems. Theoretical Computer Science, 148(2):281--301, 1995.

No context found.

P. Jancar. Undecidability of bisimilarity for Petri nets and some related problems. Theoretical Computer Science, 148(2):281--301, 1995.

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