Abstract
We consider the problem of simulation preorder/equivalence between infinite-state processes and finite-state ones. We prove that simulation preorder (in both directions) and simulation equivalence are intractable between all major classes of infinite-state systems and finite-state ones. This result is obtained by showing that the problem whether a BPA (or BPP) process simulates a finitestate one is PSPACE-hard, and the other direction is co-NP-hard; consequently, simulation equivalence between BPA (or BPP) and finite-state processes is also co-NP-hard.
The decidability border for the mentioned problem is also established. Simulation preorder (in both directions) and simulation equivalence are decidable in EXPTIME between pushdown processes and finite-state ones. On the other hand, simulation preorder is undecidable between PA and finite-state processes in both directions. The obtained results also hold for those PA and finite-state processes which are deterministic and normed, and thus immediately extend to trace preorder. Regularity (finiteness) w.r.t. simulation and trace equivalence is also shown to be undecidable for PA.
Finally, we describe a way how to utilize decidability of bisimulation problems to solve certain instances of undecidable simulation problems.We apply this method to BPP processes.
Supported by a Research Fellowship granted by the Alexander von Humboldt Foundation and by a Post-Doc grant GA ČR No. 201/98/P046.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
P.A. Abdulla and K. Čerāns. Simulation is decidable for one-counter nets. In Proceedings of CONCUR’98, volume 1466 of LNCS, pages 253–268. Springer-Verlag, 1998.
J.C.M. Baeten and W.P. Weijland. Process Algebra. Number 18 in Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, 1990.
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. Caucal. On the regular structure of prefix rewriting. Theoretical Computer Science, 106:61–86, 1992.
S. Christensen, Y. Hirshfeld, and F. Moller. Bisimulation is decidable for all basic parallel processes. In Proceedings of CONCUR’93, volume 715 of LNCS, pages 143–157. Springer-Verlag, 1993.
S. Christensen, H. Hüttel, and C. Stirling. Bisimulation equivalence is decidable for all context-free processes. Information and Computation, 121:143–148, 1995.
J.F. Groote and H. Hüttel. Undecidable equivalences for basic process algebra. Information and Computation, 115(2):353–371, 1994.
J.E. Hopcroft and J.D. Ullman. Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, 1979.
H. Hüttel. Undecidable equivalences for basic parallel processes. In Proceedings of TACS’94, volume 789 of LNCS, pages 454–464. Springer-Verlag, 1994.
P. Jančar and J. Esparza. Deciding finiteness of Petri nets up to bisimilarity. In Proceedings of ICALP’96, volume 1099 of LNCS, pages 478–489. Springer-Verlag, 1996.
P. Jančar, A. Kučera, and R. Mayr. Deciding bisimulation-like equivalences with finite-state processes. In Proceedings of ICALP’98, volume 1443 of LNCS, pages 200–211. Springer-Verlag, 1998.
P. Jančar and F. Moller. Checking regular properties of Petri nets. In Proceedings of CONCUR’95, volume 962 of LNCS, pages 348–362. Springer-Verlag, 1995.
A. Kučera. 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 and R. Mayr. Weak bisimilarity with infinite-state systems can be decided in polynomial time. Technical report TUM-I9830, Institut für Informatik, TU-München, 1998.
A. Kučera and R. Mayr. Simulation preorder on simple process algebras. Technical report TUM-I9902, Institut für Informatik, TU-München, 1999.
R. Mayr. Process rewrite systems. Information and Computation. To appear.
M.L. Minsky. Computation: Finite and Infinite Machines. Prentice-Hall, 1967.
D.E. Muller and P.E. Schupp. The theory of ends, pushdown automata, and second order logic. Theoretical Computer Science, 37(1):51–75, 1985.
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.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kučera, A., Mayr, R. (1999). Simulation Preorder on Simple Process Algebras. In: Wiedermann, J., van Emde Boas, P., Nielsen, M. (eds) Automata, Languages and Programming. Lecture Notes in Computer Science, vol 1644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48523-6_47
Download citation
DOI: https://doi.org/10.1007/3-540-48523-6_47
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66224-2
Online ISBN: 978-3-540-48523-0
eBook Packages: Springer Book Archive