Abstract
In this paper we consider the problem of comparing an arbitrary Petri net against one whose places may contain only a bounded number of tokens (that is, against a regular behaviour), with respect to trace set inclusion and equivalence, as well as simulation and bisimulation. In contrast to the known result that language equivalence is undecidable, we find that all of the above are in fact decidable. We furthermore demonstrate that it is undecidable whether a given Petri net is either trace equivalent or simulation equivalent to any (unspecified) bounded net.
The first author is supported by the Grant Agency of the Czech Republic, Grant No. 201/93/2123; and also received partial support from Esprit Network EXPRESS in order to visit the Swedish Institute of Computer Science, during which time the research reported here was carried out.
The second author is supported by Esprit Basic Research Action No. 7166, “CONCUR2”.
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Abdulla, P., K. Čerāns, P. Jančar, and F. Moller. One counter Petri nets vs bounded Petri nets. Research Report, 1995.
Christensen, S., Y. Hirshfeld, and F. Moller. Bisimulation is decidable for basic parallel processes. In E. Best (editor), Proceedings of CONCUR'93: Concurrency Theory, Lecture Notes in Computer Science 715, pp143–157, Springer-Verlag, 1993.
Dickson, L.E. Finiteness of the odd perfect and primitive abundant numbers with distinct factors. American Journal of Mathematics 35, pp413–422, 1913.
Ginsburg, S., and E. Spanier. Semigroups, Presburger formulas, and languages. Pacific Journal of Mathematics 16, pp285–296, 1966.
van Glabbeek, R.J. The linear time — branching time spectrum. In J.C.M. Baeten, and J.W. Klop (editors), Proceedings of CONCUR'90: Concurrency Theory, Lecture Notes in Computer Science 458, pp278–297, Springer-Verlag, 1990.
Higman, H. Ordering by divisibility in abstract algebras. Proceedings of the London Mathematical Society 3(2), pp326–336, 1952.
Hirshfeld, Y. Petri nets and the equivalence problem. In E. Börger, Y. Gurevich, and K. Meinke (editors), Proceedings of CSL'93: Computer Science Logic, Lecture Notes in Computer Science 832, pp165–174, Springer-Verlag, 1994.
Hopcroft, J.E., and J.D. Ullman. Introduction to Automata Theory, Languages, and Computation. Addison Wesley, 1979.
Hüttel, H. Undecidable equivalences for basic parallel processes. In R.K. Shyamasundar (editor), Proceedings of FSTTCS'93: Foundations of Software Technology and Theoretical Computer Science, Lecture Notes in Computer Science 761, Springer-Verlag, 1993.
Jančar, P. Undecidability of bisimilarity for Petri nets and some related problems. Journal of Theoretical Computer Science (to appear). (A preliminary version appears in P. Enjalbert, E.W. Mayr and K.W. Wagner (editors), Proceedings of STACS'94: Symposium on Theoretical Aspects of Computer Science, Lecture Notes in Computer Science 775, pp581–592, Springer-Verlag, 1994.)
Jančar, P. Decidability questions for equivalences on Petri nets. Czech Habilitation Thesis. Masaryk University, Brno. (Submitted April 1995.)
Karp, R., and R. Miller. Parallel program schemata. Journal of Computer and System Sciences 3, pp167–195, 1969.
Mauw, S., and H. Mulder. Regularity of BPA-systems is decidable. In B. Jonsson and J. Parrow (editors), Proceedings of CONCUR'94: Concurrency Theory, Lecture Notes in Computer Science 836, pp34–47, Springer-Verlag, 1993.
Mayr, E. An algorithm for the general Petri net reachability problem. SIAM Journal of Computing 13, pp441–460, 1984.
Mazurkiewicz, A. Trace theory. In W. Brauer, W. Reisig, and G. Rozenberg (editors), Petri Nets: Applications and Relationships to Other Models of Concurrency, Lecture Notes in Computer Science 255, pp279–324, Springer-Verlag, 1987.
Milner, R. Communication and Concurrency. Prentice Hall, 1989.
Minsky, M. Computation: Finite and Infinite Machines. Prentice Hall, 1967.
Peterson, J.L. Petri Net Theory and the Modeling of Systems. Prentice Hall, 1981.
Stirling, C. Local model checking games. Department of Computer Science Research Report, University of Edinburgh, 1995.
Valk, R., and G. Vidal-Naquet. Petri nets and regular languages. Journal of Computer and System Sciences 23(3), pp299–325, 1981.
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Jančar, P., Moller, F. (1995). Checking regular properties of Petri nets. In: Lee, I., Smolka, S.A. (eds) CONCUR '95: Concurrency Theory. CONCUR 1995. Lecture Notes in Computer Science, vol 962. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60218-6_26
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DOI: https://doi.org/10.1007/3-540-60218-6_26
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