Abstract
We define a class of transition systems called effective commutative transition systems (ECTS) and show, by generalising a tableaubased proof for BPP, that strong bisimilarity between any two states of such a transition system is decidable. It gives a general technique for extending decidability borders of strong bisimilarity for a wide class of in.nite-state transition systems. This is demonstrated for several process formalisms, namely BPP process algebra, lossy BPP processes, BPP systems with interrupt and timed-arc BPP nets.
The author is supported in part by the GACR, grant No. 201/00/0400.
Basic Research in Computer Science, Centre of the Danish National Research Foundation.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
P.A. Abdulla and B. Jonsson. Verifying programs with unreliable channels. Information and Computation, 127(2):91–101, 1996.
J.C.M. Baeten, J.A. Bergstra, and J.W. Klop. Syntax and defining equations for an interrupt mechanism in process algebra. Fundamenta Informaticae, IX(2):127–168, 1986.
J.C.M. Baeten and J.A. Bergstra. Mode transfer in process algebra. Technical report CSR 00-01, Vakgroep Informatica, Technische Universiteit Eindhoven, 2000.
B. Berard, A. Labroue, and Ph. Schnoebelen. Verifying performance equivalence for timed basic parallel processes. In Proc. of FOSSACS’2000, volume 1784 of LNCS, p. 35–47. Springer-Verlag, 2000.
J.A. Bergstra. A mode transfer operator in process algebra. Technical report P8808b, University of Amsterdam, The Netherlands, 1989.
T. Bolognesi, F. Lucidi, and S. Trigila. From timed Petri nets to timed LOTOS. In Proc. of the IFIP WG 6.11 0th International Symposium on Protocol Specification, Testing and Verification, p. 1–14. Amsterdam, 1990.
A. Bouajjani and R. Mayr. Model checking lossy vector addition systems. In Proc. of STACS’99, volume 1563 of LNCS, p. 323–333. Springer-Verlag, 1999.
O. Burkart, D. Caucal, F. Moller, and B. Steffen. Verification on infinite structures. In J. Bergstra, A. Ponse, and S. Smolka, editors, Handbook of Process Algebra, chapter 9, p. 545–623. Elsevier Science, 2001.
S. Christensen. Decidability and Decomposition in Process Algebras. PhD thesis, The University of Edinburgh, 1993.
S. Christensen, Y. Hirshfeld, and F. Moller. Bisimulation is decidable for basic parallel processes. In Proc. of CONCUR’93, volume 715 of LNCS, p. 143–157. Springer-Verlag, 1993.
T. Cobben and A. Engels. Disrupt and interrupt in MSC: Possibilities and problems. In Proc. of the 1st Workshop of the SDL Forum Society on SDL and MSC, number 104 in Informatik-Berichte, p. 75–83. 1998.
L.E. Dickson. Finiteness of the odd perfect and primitive abundant numbers with distinct factors. American Journal of Mathematics, 35:413–422, 1913.
B. Diertens. New features in PSF I: Interrupts, disrupts, and priorities. Technical report P9417, University of Amsterdam, The Netherlands, 1994.
H.M. Hanisch. Analysis of place/transition nets with timed-arcs and its application to batch process control. In Application and Theory of Petri Nets, volume 691 of LNCS, p. 282–299, 1993.
P. Jancar. Undecidability of bisimilarity for Petri nets and some related problems. Theoretical Computer Science, 148(2):281–301, 1995.
P. Jancar and F. Moller. Techniques for decidability and undecidability of bisimilarity-an invited tutorial. In Proc. of CONCUR’ 99, volume 1664 of LNCS, p. 30–45. Springer-Verlag, 1999.
R. Mayr. Process rewrite systems. Information and Comp., 156(1):264–286, 2000.
R. Mayr. Undecidable problems in unreliable computations. In Proc. of LATIN’00, volume 1776 of LNCS. Springer-Verlag, 2000.
R. Milner. Communication and Concurrency. Prentice-Hall, 1989.
V. Valero Ruiz, D. de Frutos Escrig, and O. Marroquin Alonso. Decidability of properties of timed-arc Petri nets. In ICATPN 2000, volume 1825 of LNCS, p. 187–206. Springer-Verlag, 2000.
J. Srba. Basic process algebra with deadlocking states. Theoretical Computer Science, 266(1–2):605–630, 2001.
J. Srba. Note on the tableau technique for commutative transition systems. Technical Report RS-01-50, BRICS Research Series, 2001.
J. Srba. Strong bisimilarity and regularity of basic parallel processes is PSPACEhard. In Proc. of STACS’02, LNCS. Springer-Verlag, 2002. To appear.
C. Stirling. Decidability of weak bisimilarity for a subset of basic parallel processes. In Proc. of FOSSACS’01, volume 2030 of LNCS, p. 379–393. Springer-Verlag, 2001.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Srba, J. (2002). Note on the Tableau Technique for Commutative Transition Systems. In: Nielsen, M., Engberg, U. (eds) Foundations of Software Science and Computation Structures. FoSSaCS 2002. Lecture Notes in Computer Science, vol 2303. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45931-6_27
Download citation
DOI: https://doi.org/10.1007/3-540-45931-6_27
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43366-8
Online ISBN: 978-3-540-45931-6
eBook Packages: Springer Book Archive