Abstract
We examine the problem of finite-state representability of infinite-state processes w.r.t. certain behavioural equivalences. We show that the classical notion of regularity becomes insufficient in case of all equivalences of van Glabbeek's hierarchy except bisimilarity, and we design and justify a generalization in the form of strong regularity and finite characterizations. We show that the condition of strong regularity guarantees an existence of finite characterization in case of all equivalences of van Glabbeek's hierarchy, and we also demonstrate that there are behaviours which are regular but not strongly regular w.r.t. all equivalences of the mentioned hierarchy except bisimilarity.
Supported by GA ČR, grant number 201/97/0456
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References
O. Burkart, D. Caucal, and B. Steffen. Bisimulation collapse and the process taxonomy. In Proceedings of CONCUR'96, volume 1119 of LNCS, pages 247–262. Springer-Verlag, 1996.
D.J.B. Bosscher and W.O.D. Griffionen. Regularity for a large class of context-free processes is decidable. In Proceedings of ICALP'96 [Ica96], pages 182–192.
I. Čer ná, M. Křetínský, and A. Kučera. Bisimilarity is decidable in the union of normed BPA and normed BPP processes. Electronic Notes in Theoretical Computer Science, 6, 1997.
Proceedings of ICALP'96, volume 1099 of LNCS. Springer-Verlag, 1996.
P. Jancar. Bisimulation equivalence is decidable for one-counter processes. In Proceedings of ICALP'97, volume 1256 of LNCS pages 549–559. Springer-Verlag, 1997.
P. Jančar and J. Esparza. Deciding finiteness of Petri nets up to bisimilarity In Proceedings of ICALP'96 [Ica96], pages 478–489.
A. Kucera. Regularity is decidable for normed PA processes in polynomial time. In Proceedings of FST&TCS'96, volume 1180 of LNCS, pages 111–122. Springer-Verlag, 1996.
A. Kučera. How to parallelize sequential processes. In Proceedings of CONCUR'97, volume 1243 of LNCS, pages 302–316. Springer-Verlag, 1997.
R. Milner. Communication and Concurrency. Prentice-Hall, 1989.
S. Mauw and H. Mulder. Regularity of BPA-systems is decidable. In Proceedings of CONCUR'94, volume 836 of LNCS pages 34–47. Springer-Verlag, 1994.
R.J. van Glabbeek. The linear time—branching time spectrum. In Proceedings of CONCUR'90, volume 458 of LNCS pages 278–297. Springer-Verlag, 1990.
R.J. van Glabbeek and W.P. Weijland. Branching time and abstraction in bisimulation semantics. Information Processing 89, pages 613–618, 1989.
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Kučera, A. (1997). On finite representations of infinite-state behaviours. In: Plášil, F., Jeffery, K.G. (eds) SOFSEM'97: Theory and Practice of Informatics. SOFSEM 1997. Lecture Notes in Computer Science, vol 1338. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63774-5_129
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DOI: https://doi.org/10.1007/3-540-63774-5_129
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