Abstract
We consider the factorization (collapse) of infinite transition graphs wrt. bisimulation equivalence. It turns out that almost none of the more complex classes of the process taxonomy, which has been established in the last years, are preserved by this operation. However, for the class of BPA graphs (i.e. prefix transition graphs of context-free grammars) we can show that the factorization is effectively a regular graph, i.e. finitely representable by means of a deterministic hypergraph grammar. Since finiteness of regular graphs is decidable, this yields, as a corollary, a decision procedure for the finiteness problem of context-free processes wrt. bisimulation equivalence.
Supported by the European Community under HCM grant ERBCHBGCT 920017.
Supported by Esprit BRA 6317 (ASMICS).
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J.C.M. Baeten, J.A. Bergstra, and J.W. Klop. Decidability of Bisimulation Equivalence for Processes Generating Context-Free Languages. In PARLE '87, LNCS 259, pages 94–113. Springer, 1987.
O. Burkart, D. Caucal, and B. Steffen. An Elementary Bisimulation Decision Procedure for Arbitrary Context-Free Processes. In MFCS '95, LNCS 969, pages 423–433. Springer, 1995.
D.J.B. Bosscher and W.O.D. Griffioen. Regularity for a Large Class of Context-Free Processes is Decidable. Will be presented at ICALP '96, 1996.
R. Büchi. Regular Canonical Systems. Archiv für Mathematische Logik und Grundlagenforschung, 6:91–111, 1964.
D. Caucal. Graphes Canoniques de Graphes Algébriques. RAIRO, 24(4):339–352, 1990.
D. Caucal. On the Regular Structure of Prefix Rewriting. Theoretical Computer Science, 106:61–86, 1992.
S. Christensen, Y. Hirshfeld, and F. Moller. Bisimulation Equivalence is Decidable for all Basic Parallel Processes. In CONCUR '93, LNCS 715, pages 143–157. Springer, 1993.
S. Christensen, Y. Hirshfeld, and F. Moller. Decomposability, Decidability and Axiomatisability for Bisimulation Equivalence on Basic Parallel Processes. In LICS '93. IEEE Computer Society Press, 1993.
S. Christensen. Decidability and Decomposition in Process Algebras. PhD thesis, The University of Edinburgh, Department of Computer Science, 1993.
S. Christensen, H. Hüttel, and C. Stirling. Bisimulation Equivalence is Decidable for all Context-Free Processes. In CONCUR '92, LNCS 630, pages 138–147. Springer, 1992.
D. Caucal and R. Monfort. On the Transition Graphs of Automata and Grammars. In Graph-Theoretic Concepts in Computer Science, LNCS 484, pages 311–337. Springer, 1990.
J.F. Groote. A Short Proof of the Decidability of Bisimulation for Normed BPA-Processes. Information Processing Letters, 42:167–171, 1991.
Y. Hirshfeld, M. Jerrum, and F. Moller. A Polynomial Algorithm for Deciding Bisimilarity of Normed Context-Free Processes. In FOCS '94, pages 623–631. IEEE Computer Society Press, 1994.
Y. Hirshfeld and F. Moller. A Fast Algorithm for Deciding Bisimilarity of Normed Context-Free Processes. In CONCUR '94, LNCS 836, pages 48–63. Springer, 1994.
H. Hüttel and C. Stirling. Actions Speak Louder than Words: Proving Bisimilarity for Context-Free Processes. In LICS '91, pages 376–386. IEEE Computer Society Press, 1991.
P. Jančar and J. Esparza. Deciding Finiteness of Petri Nets up to Bisimulation. Will be presented at ICALP '96, 1996.
P. Jančar and F. Moller. Checking Regular Properties of Petri Nets. In CONCUR '95, LNCS 995, pages 348–362. Springer, 1995.
S. Mauw and H. Mulder. Regularity of BPA-Systems is Decidable. In CONCUR '94, LNCS 836, pages 34–47. Springer, 1994.
C. Stirling. Decidability of Bisimulation Equivalence for Normed Pushdown Processes. Will be presented at CONCUR '96, 1996.
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Burkart, O., Caucal, D., Steffen, B. (1996). Bisimulation collapse and the process taxonomy. In: Montanari, U., Sassone, V. (eds) CONCUR '96: Concurrency Theory. CONCUR 1996. Lecture Notes in Computer Science, vol 1119. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61604-7_59
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DOI: https://doi.org/10.1007/3-540-61604-7_59
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