Checking Equivalences Between Concurrent Systems of Finite Agents (Extended Abstract)

Consider two synchronously communicating systems p and q over finite agents. Assume that one wants to check whether p ∼ q for one of the commonly used equivalences. We show that this question is PSPACE hard for all equivalences which lie between strong bisimulation and trace equivalences. For some equivalences exponential lower and upper bounds are proven. We also show that this problem is NP hard and co-NP hard even for a class of very simple finite agents.

[1]  Jan Friso Groote,et al.  An Efficient Algorithm for Branching Bisimulation and Stuttering Equivalence , 1990, ICALP.

[2]  Robin Milner,et al.  Communication and concurrency , 1989, PHI Series in computer science.

[3]  李幼升,et al.  Ph , 1989 .

[4]  C. A. R. Hoare,et al.  A Theory of Communicating Sequential Processes , 1984, JACM.

[5]  Martin Fürer.  The Complexity of the Inequivalence Problem for Regular Expressions with Intersection , 1980, ICALP.

[6]  Scott A. Smolka,et al.  CCS expressions, finite state processes, and three problems of equivalence , 1983, PODC '83.

[7]  Bloom Bard,et al.  Ready simulation, bisimulation, and the semantics of CCS-like languages , 1989 .

[8]  C. A. R. Hoare,et al.  Communicating sequential processes , 1978, CACM.

[9]  Robert E. Tarjan,et al.  Three Partition Refinement Algorithms , 1987, SIAM J. Comput..

[10]  Albert R. Meyer,et al.  Word problems requiring exponential time(Preliminary Report) , 1973, STOC.

[11]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[12]  David Park,et al.  Concurrency and Automata on Infinite Sequences , 1981, Theoretical Computer Science.

[13]  守屋 悦朗,et al.  J.E.Hopcroft, J.D. Ullman 著, "Introduction to Automata Theory, Languages, and Computation", Addison-Wesley, A5変形版, X+418, \6,670, 1979 , 1980 .

[14]  Alain J. Mayer,et al.  Word Problems - This Time with Interleaving , 1991 .

[15]  José L. Balcázar,et al.  Parallel Complexity in the Design and Analysis on Conurrent Systems , 1991, PARLE.

[16]  Scott A. Smolka,et al.  CCS expressions, finite state processes, and three problems of equivalence , 1983, PODC '83.

[17]  H. Arbeláez,et al.  Korth cm. International business : environment and management. Prentice hall, inc, englewood cliffs, 1985, 2a ed , 1985 .

[18]  Matthew Hennessy,et al.  Algebraic theory of processes , 1988, MIT Press series in the foundations of computing.

[19]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[20]  Harry B. Hunt,et al.  The Equivalence Problem for Regular Expressions with Intersection is Not Polynomial in Tape , 1973 .

[21]  N. S. Barnett,et al.  Private communication , 1969 .