Hirshfeld, Y.: "Petri Nets and the Equivalence Problem". Proceedings of CSL '93, E. Borger, Y. Gurevich and K. Meinke (eds.), Lecture Notes in Computer Science 832, 1994, 165--174.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....D. Ranganayakulu SIVET College Gowrivakkam nayakulu imsc.ernet.in K. Rangarajan Madras Christian College Tambaram Chennai 600 059, India Abstract. We give precise syntactic characterizations for the following subclasses of 1 safe net systems: S systems [12] communication free systems [13] and N free systems (following [16] by proving Kleene Myhill Nerode B uchi theorems. Keywords: Series parallel, poset, pomset, languages, Petri nets, 1 safe nets. Let A be a nite nonempty alphabet. A nite state machine accepts runs which can be described by terms over A in a suitable ....

....and Algebra in Concurrency, Dresden, 2000. FC) systems [12] Behavioural characteristics of these subclasses have also been examined (see [4] for a detailed study) We characterize two subclasses of nets which fall within the ambit of sp languages: S systems and communication free (CF) systems [13]. We de ne two natural subclasses of sp languages, the right and outermost sp languages, and show that the rsp and osp languages accepted by 1 safe nets can be accepted by 1 safe CF and S systems respectively. They are also characterized in terms of algebra, logic and syntactic expressions. ....

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Y. Hirshfeld. Petri nets and the equivalence problem, Proc. CSL, Swansea (E. B orger, Y. Gurevich, K. Meinke, eds.), LNCS 832 (1994) 165-174.

.... bisimilarity for BPP and even for BPP , extension of BPP by communication, was given in [10] The PSPACE lower bound has been recently proved in [28] followed by the PSPACEcompleteness result of Jan car [20] On the other hand, all other equivalences in van Glabbeek s spectrum are undecidable [17, 19]. BPP is the natural class of processes to investigate non interleaving equivalences, intended to capture true concurrent computations of a system. One of the bisimulationlike non interleaving equivalences is distributed bisimilarity [6] taking into account spatial distribution of a process. ....

Y. Hirshfeld. Petri nets and the equivalence problem. In Proc. Computer Science Logic (CSL'93), LNCS 832, pages 165--174, 1993.

.... bisimilarity for BPP and even for BPP , extension of BPP by communication, was given in [10] The PSPACE lower bound has been recently proved in [28] followed by the PSPACE completeness result of Jan car [20] On the other hand, all other equivalences in van Glabbeek s spectrum are undecidable [17, 19]. BPP is the natural class of processes to investigate non interleaving equivalences, intended to capture true concurrent computations of a system. One of the bisimulation like non interleaving equivalences is distributed bisimilarity [6] taking into account spatial distribution of a process. ....

Y. Hirshfeld. Petri nets and the equivalence problem. In Proc. Computer Science Logic (CSL'93), LNCS 832, pages 165--174, 1993.

....infinite state systems. An elegant proof of decidability of bisimilarity for BPP and even for BPP , extension of BPP by communication, was given in [10] The PSPACE lower bound has been recently proved in [28] On the other hand, all other equivalences in van Glabbeek s spectrum are undecidable [18, 20]. BPP is a very natural class of processes to investigate non interleaving equivalences, intended to capture true concurrent computations of a system. One of the bisimulation like non interleaving equivalences is distributed bisimilarity [6] taking into account spatial distribution of a ....

Y. Hirshfeld. Petri nets and the equivalence problem. In Proc. Computer Science Logic (CSL'93), LNCS 832, pages 165--174, 1993.

....composition. Strong bisimilarity [19] is a well accepted behavioural equivalence which often remains decidable for infinite state systems. An elegant proof of decidability of bisimilarity for BPP was given in [8] while all other equivalences in van Glabbeek s spectrum are undecidable in BPP [15, 17]. In order to deal with timing aspects of systems, process algebras were extended with an appropriate notion of time (see e.g. 20] 1] 14] 10] 9] 2] A substantial effort have also been directed toward defining a robust notion of equivalence taking performance into consideration, e.g. ....

Y. Hirshfeld. Petri nets and the equivalence problem. In Proc. Computer Science Logic (CSL'93), LNCS 832, pages 165--174, 1993.

....BPPs can hence be seen as arising from a minimal concurrent extension of finite automata and therefore a natural starting point of exploring infinite state systems. Another reason for studying BPP is its close connection to communication free nets, a natural subclass of labelled Petri nets [4, 10]. It was hence shown in [4] that any BPP process can be effectively transformed into an equivalent BPP process in full standard form while preserving bisimilarity. Moreover, there is an obvious isomorphism between the transition system of a BPP process in full standard form and the labelled ....

....with respect to any interleaving equivalence coarser than or equal to bisimilarity. BPPs were first suggested in [4, 6] and accompanied by a positive result stating that (strong) bisimulation is decidable on BPP. Later Hirshfeld showed that in contrast language (trace) equivalence is undecidable [10] for BPP. The picture has since been completed by a result showing that in the branching time linear time spectrum of [30] only bisimulation is decidable, see [12] For a survey on results for infinite state systems see [5] Also, various generalizations of behavioural equivalences to deal with ....

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Y. Hirshfeld, Petri Nets and the Equivalence Problem, CSL '93, Springer LNCS 882, 165--174 (1994).

....was based on pomsets representing global causal dependency [22] and the second known as location equivalence on locality [4] representing spatial distribution of events. The two notions of non interleaving equivalences were shown to be decidable on BPP contrasting the result of Hirshfeld [10] that language equivalence is undecidable. Moreover, larger subclasses of CCS and TCSP obtained by adding di erent means for communication were studied. It was hence shown that when adding the parallel combinator of Milner s CCS to BPP, BPPM , we keep the decidability of both location and pomset ....

....by a reduction to the halting problem for two counter machines base on weak encodings of counter machines. Our results are summarised in the table below where yes indicates decidability and no undecidability. The results of the rst column are all direct consequences of Hirshfeld s result on BPP [10]. The second and third show our results: BPP renaming and=or hiding no yes yes BPP S no no yes BPP S renaming and=or hiding no no no Furthermore, we turn to the weak case. We consider three extensions: BPP with pre xing BPP , BPP with CCS communication BPPM , and BPP with both pre ....

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Y Hirshfeld. Petri nets and the equivalence problem. In E. Borger, Y. Gurevich, and K. Meinke, editors, Computer Science Logic: 7th Workshop, CSL '93 Selected Papers, pages 165-174. Springer-Verlag, 1994. Lecture Notes in Computer Science, Vol. 832.

....way. For example, for the class of Petri nets in which every transition has a single input place the so called Basic Parallel Processes strong bisimulation equivalence is decidable [1] whereas all other standard equivalences (such as trace equivalence) are undecidable, even in the strong case [6, 8]. If on the other hand we compare two bounded Petri nets, then these equivalences all become decidable, as such nets describe behaviours realized by finite automata. We consider here the problem of restricting just one of the two Petri nets to be bounded, thus comparing general Petri nets against ....

....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 extension of the ....

Y. Hirshfeld, Petri nets and the equivalence problem, in "Computer Science Logic: CSL'93," (E. Borger, Y. Gurevich and K. Meinke, eds.), Lecture Notes in Computer Science, Vol 832, Springer-Verlag, Berlin/New York, 1994.

....by Hirshfeld and Moller [24] Finally, Christensen, Huttel and Stirling [13,14] demonstrate the general problem to be decidable, whilst Burkart, Caucal and Steffen [5] provide an elementary decision procedure. For the case of commutative context free automata BPP, we get similar results. Hirshfeld [19] demonstrates the undecidability of language equivalence, and Huttel [25] extends this undecidability result to all of van Glabbeek s equivalences except bisimilarity. Christensen, Hirshfeld and Moller [11,12] demonstrate the decidability of bisimilarity, first for the normed case and then in the ....

Y. Hirshfeld (1993). Petri Nets and the Equivalence Problem. Proceedings of CSL'93, Lecture Notes in Computer Science 832:165--174.

....time for normed BPA [69, 70] and normed BPP [71] These results contrast with those regarding the undecidability of language equivalence for both BPA and BPP. The negative result for BPA [6] follows from the fact that BPA effectively defines the class of context free languages; and that for BPP [66] follows from a modification by Hirshfeld of a technique of Jancar which is described in Section 2.4. Both arguments can be shown to hold for the class of normed systems. Also, for both BPA and BPP, this undecidability extends to all equivalences which lie in Glabbeek s spectrum [59] between ....

....undecidability results for bisimilarity through mimicking Minsky machines in a weak fashion but faithfully enough to capture the essence of the halting problem. Jancar first employed his ideas to demonstrate the undecidability of bisimulation equivalence over the class of Petri nets. Hirshfeld [66] modified the argument to demonstrate the undecidability of trace equivalence over BPP. Jancar and Moller [89] then used the technique to demonstrate the undecidability of regularity checking of Petri nets with respect to both simulation and trace equivalence. In the following we generalize ....

Y. Hirshfeld. Petri nets and the equivalence problem. In E. Borger, Y. Gurevich, and K. Meinke, editors, CSL'93, LNCS 832, pages 165--174, Swanseea, 1993. Springer.

....of) in Thetanite state systems has been attracting attention for almost a 5 decade; here we only mention some of the most relevant results. First, it was shown in [GH94] that the problems BPA v s BPA and BPA = s BPA are undecidable. The undecidability of BPP v s BPP and BPP = s BPP was proved in [Hir94] An interesting positive result is [A i C98] where it is shown that OC N v s OC N (and hence also OC N = s OC N) is decidable. However, OC A v s OC A and OC A = s OC A are already undecidable [JMS99] The problem of checking simulation between in Thetanite and Thetanitestate systems was ....

Y. Hirshfeld. Petri nets and the equivalence problem. In Proceedings of CSL'93, volume 832 of Lecture Notes in Computer Science, pages 165#174. Springer, 1994.

....of) infinite state systems has been attracting attention for almost a 5 decade; here we only mention some of the most relevant results. First, it was shown in [GH94] that the problems BPA v s BPA and BPA = s BPA are undecidable. The undecidability of BPP v s BPP and BPP = s BPP was proved in [Hir94] An interesting positive result is [A C98] where it is shown that OC N v s OC N (and hence also OC N = s OC N) is decidable. However, OC A v s OC A and OC A = s OC A are already undecidable [JMS99] The problem of checking simulation between infinite and finitestate systems was first examined ....

Y. Hirshfeld. Petri nets and the equivalence problem. In Proceedings of CSL'93, volume 832 of Lecture Notes in Computer Science, pages 165--174. Springer, 1994.

....way. For example, for the class of Petri nets in which every transition has a single input place the so called Basic Parallel Processes strong bisimulation equivalence is decidable [1] whereas all other standard equivalences (such as trace equivalence) are undecidable, even in the strong case [6, 8]. If on the other hand we compare two bounded Petri nets, then these equivalences all become decidable, as such nets describe behaviours realized by finite automata. We consider here the problem of restricting just one of the two Petri nets to be bounded, thus comparing general Petri nets against ....

....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 of the ....

Y. Hirshfeld, Petri nets and the equivalence problem, in "Computer Science Logic: CSL'93," (E. Borger, Y. Gurevich and K. Meinke, eds.), Lecture Notes in Computer Science, Vol 832, Springer-Verlag, Berlin/New York, 1994.

.... bisimilarity is undecidable for Petri nets. As for the trace equivalence, its undecidability for Petri nets has been known from [6] in fact, 12] also provides a more direct proof of this undecidability. It is interesting that the trace equivalence is undecidable even for BPP; it is shown in [7] by a clever modi cation of the technique of [12] Remark. In [11] another modi cation was added to show undecidability for other equivalences in the linear time branching time spectrum of [5] on BPP. On the other hand, decidability results for some ner versions of bisimilarity on BPP have ....

Y. Hirshfeld, Petri nets and the equivalence problem, in: Proc. Computer Science Logic '93, Lecture Notes in Computer Science, Vol. 832 (SpringerVerlag, 1994) 165-174.

....not put any bound on the number of unbounded places. The above discussion shows that the technique of the proof for bisimilarity also provides new, technically simpler, proofs for stronger versions of some known results. The results of this paper rst appeared in the report [17] Later Hirshfeld ([12]) followed the general strategy having to invent the appropriate modi cations to show the undecidability of the language equivalence problem even for the subclass of Petri nets where each transition has one input place only; i.e. in fact, for the above mentioned BPP. H uttel [15] then ....

....2 unbounded places. For the case with 1 unbounded place, I conjecture that the bisimulation equivalence is semilinear and that both problems are decidable. In this sense, the decidability border would be established precisely. But there are other kinds of the border. As mentioned, Hirshfeld in [12] shows that BPP like Petri nets are sucient for the undecidability of language equivalence; on the contrary, bisimilarity is decidable for them ( 4] It is also not dicult to modify the proofs in this paper in order to show the undecidability results for self loop free Petri nets, and for single ....

Y. Hirshfeld, Petri nets and the equivalence problem, in: Proc. Computer Science Logic '93, Lecture Notes in Computer Science, Vol. 832 (SpringerVerlag, 1994) 165-174.

....Christensen, Hirshfeld and Moller have proved [11, 10] that bisimulation equivalence by using a tableau technique similar to the one in this paper. Again, a by product of the decision procedure is a sound and complete sequent style equational theory for bisimilarity. Recent results indicate [17] that all other known equivalences are undecidable for BPP; bisimulation equivalence seems to have a very special status as far as decidability is concerned. However, even when a slight extensions of BPP is considered, namely that of restriction, bisimilarity also becomes undecidable [9] An ....

Y. Hirshfeld. Finitely generated processes, petri nets and the equivalence problem. Unpublished note, May 1993.

....is a sound and complete sequent based equational theory for bisimilarity A natural question is whether the other equivalences within van Glabbeek s linear time branching time hierarchy are decidable. Recently, Yoram Hirshfeld has shown that language equivalence is undecidable for BPP (see [Hir93]) The proof relies on showing that ctr(E 1 ) ctr(E 2 ) ctr(E) consists of the completed traces for E) if and only if ctr(E 1 E 2 ) ctr(E 2 ) and then showing language inclusion to be undecidable on BPP. This, in turn, is achieved by a reduction from the Halting problem and relies on a ....

....below bisimilarity in the van Glabbeek hierarchy are decidable for BPP. For most of the equivalences, this is a direct consequence of the undecidability of ready simulation equivalence as this equivalence is near the top of the hierarchy. The reduction is based on an idea due to Hirshfeld [Hir93]. Thus the decidability records for the two (incomparable) process classes BPA and BPP are surprisingly similar: for both calculi, bisimilarity is decidable while all the other equivalences in the van Glabbeek hierarchy are undecidable. 5 Whither infinite transition graphs Lately, following work ....

Y. Hirshfeld. Finitely generated processes, petri nets and the equivalence problem. In Proceedings of CSL 93, 1993.

.... For example, for the class of Petri nets in which every transition has a single input place the so called Basic Parallel Processes strong bisimulation equivalence is decidable [1] whereas all other standard equivalences (such as trace equivalence) are undecidable, even in the strong case [6, 8]. If on the other hand we compare two bounded Petri nets, then these equivalences all become decidable, as such nets describe behaviours depicted by finite automata. We consider here the problem of restricting just one of the two Petri nets to be bounded, thus comparing general Petri nets against ....

....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 extension of the ....

Hirshfeld, Y. Petri nets and the equivalence problem. In E. Borger, Y. Gurevich and K. Meinke (editors), Proceedings of CSL'93: Computer Science Logic, Lecture Notes in Computer Science 832:165--174, Springer-Verlag, 1994.

....equivalence notions for infinite state systems has been extensively studied in the last years. Among other results, it has been shown that trace equivalence is undecidable for Basic Process Algebra (BPA) and Basic Parallel Processes (BPP) while bisimulation equivalence is decidable in both cases [1, 2, 4]. For arbitrary labelled Petri nets (called just Petri nets in the rest of this introduction) all the equivalence notions commonly used in the literature are undecidable [8, 6] Therefore, in order to obtain positive results some constraints have to be imposed on the nets accepted as problem ....

....finiteness problem for Basic Process Algebra has been recently studied in [10] The results are similar to ours: undecidable for trace equivalence, but decidable for bisimulation equivalence. Finally, since BPPs are bisimilar to a particular class of Petri nets (called communication free nets in [4]) the decidability of the finiteness problem for BPP and bisimulation follows as a corollary of our results. ....

Y. Hirshfeld. Petri Nets and the Equivalence Problem. In Proceedings of CSL '93, LNCS 832, 165--174, 1994.

....and understand the decidability boundaries for bisimilarity, which are different from those for language equivalence. It is e.g. known that bisimilarity is decidable for Basic Parallel Processes, BPP (Christensen, Hirshfeld, and Moller, 1993) while language equivalence is undecidable for them (Hirshfeld, 1994). More relevant here are context free processes (generated by context free grammars) also called BPA processes, where language equivalence is well known to be undecidable while bisimilarity is decidable (Christensen, Huttel, and Stirling, 1995) Pushdown automata (which are in the language ....

Hirshfeld Y. (1994), Petri nets and the equivalence problem, in "Proceedings, Computer Science Logic (CSL)'93," Lecture Notes in Computer Science, Vol. 832, Springer-Verlag, pp. 165--174.

....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 communication free 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 freely through the net independently of each other. We obtain a structural characterisation of the set ....

Hirshfeld, Y.: "Petri Nets and the Equivalence Problem". Proceedings of CSL '93, E. Borger, Y. Gurevich and K. Meinke (eds.), Lecture Notes in Computer Science 832, 1994, 165--174.

....the projection of the sequence of states reached along the prefix on the set of meaningful states corresponds to the computation of the counter machine M. It is clear that M has honest runs, but not every run of M is honest. A second weak model. Following an idea introduced by Hirshfeld in [13], we split the actions of the first model. A counter c j is now modelled by C j def = dec 1 j Delta dec 2 j Delta dec 3 j Delta 0 A state q i of type II is modelled by SQ i def = in 1 i Delta (Q i k SQ i ) Q i def = out 1 i Delta out 2 i Delta 0 In the other equations we ....

Y. Hirshfeld. Petri Nets and the Equivalence Problem. In Proceedings of CSL '93, 1994.

....equivalence to a finite state LTS (see section 3) and model checking with the weak branching time temporal logic UB Gamma of section 4. On the other hand BPP are powerful enough to make some properties undecidable, like model checking with the modal calculus [4] and language equivalence [6]. Acknowledgement Many thanks to Javier Esparza for helpful discussions. ....

Y. Hirshfeld. Petri nets and the equivalence problem. In Proceedings of CSL'93, number 832 in LNCS, pages 165--174. Springer Verlag, 1993.

....certain action, the second process is able to respond by performing the same action, and vice versa. The notion of bisimulation equivalence was introduced by Park [13] as a notion of behavioural equivalence between concurrent systems, and has been intensively studied in the intervening years; see [1, 2, 3, 4, 5, 6, 7, 9, 10, 12] for just some of the work in this area which is relevent to our present study. Bisimulation equivalence plays an important role in algebraic theories of concurrency, such as that of Milner [11] Bisimulation equivalence in the context of BPP differs from language equivalence of context free ....

....of decidability is a real one. Indeed, the somewhat related question of language equivalence of context free grammars has long been known to be undecidable [8] while the more closely related question of deciding trace equivalence for normed BPP was recently shown to be undecidable by Hirshfeld [6]. The time complexity of the decision procedure of Christensen et al. is not known to be bounded by any primitive recursive function. In this article we present (see Theorem 2) the first polynomial time algorithm for deciding bisimulation equivalence for normed BPP: indeed the first decision ....

Y. Hirshfeld, Petri nets and the equivalence problem. To appear in Proceedings of CSL 93 (Karl Meinke, ed.), Springer Lecture Notes in Computer Science.

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Hirshfeld, Y.: "Petri Nets and the Equivalence Problem". Proceedings of CSL '93, E. Borger, Y. Gurevich and K. Meinke (eds.), Lecture Notes in Computer Science 832, 1994, 165--174.

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Y. Hirshfeld. Petri Nets and the Equivalence Problem. In Proceedings of CSL '93, 1994.

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Y. Hirshfeld. Petri nets and the equivalence problem. In Proceedings of CSL '93, LNCS 832:165--180, 1994.

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Hirshfeld, Y. Petri nets and the equivalence problem. In E. Borger, Y. Gurevich and K. Meinke (editors), Proceedings of CSL'93: Computer Science Logic, Lecture Notes in Computer Science 832:165--174, Springer-Verlag, 1994.

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Y. Hirshfeld. Petri nets and the equivalence problem. In Proceedings of the 7th Workshop on Computer Science Logic (CSL'93), volume 832 of LNCS, pages 165--174. Springer-Verlag, 1993.

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