Abstract
We study the complexity of the following three relational problems: Let ∼ be a binary relation on finite state processes; let p 0 be a fixed finite state process; and let π be a nontrivial predicate on finite state processes such that x and y are weakly bisimilar implies π(x) = π(y). (i) P 1: Determine for processes p and q, if p ∼ q; (ii) P 2 Determine for process p, if p ∼ p 0; and (iii) P 3: Determine for process p, if π(p) = true. We study the complexities of these problems, when processes are represented by sequential transition systems and by parallel composition of transition systems (with and without hiding). A number of results are obtained for both representations.
This research was supported by NSF Grants CCR-90-06396 and CCR-94-06611.
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References
W.F. Dowling and J.H. Gallier. Linear time algorithm for testing the satisfiability of propositional horn formulae. Journal of Logic Programming, 3:267–284, 1984.
M. Garey and D. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, SanFrancisco, 1979.
R. Greenlaw, H. J. Hoover, and W. L. Ruzzo. Limits to Parallel Computation: P-completeness Theory. Oxford University Press, 1995.
C. A. R. Hoare. Communicating Sequential Processes. Prentice Hall International, 1984.
Dung T. Huynh and Lu Tian. On deciding some equivalences for concurrent processes. Theoretical Informatics and Applications, 28(1):51–71, 1994.
R. Kurshan. Computer Aided Verification of Coordinating processes: An Automata Theoretic Approach. Princeton University Press, 1994.
Nancy Lynch and Frits Vaandrager. Forward and backward simulations-part i: Untimes systems. Information and Computation, 1995.
R. Milner. Communication and Concurrency. International Series in Computer Science. Prentice Hall, 1989. SU Fisher Research 511/24.
A. Rabinovich. Checking equivalences between concurrent systems of finite state agents. In ICALP, Lecture Notes in Computer Science 623, pages 696–707, 1992. A more recent draft is available from the author (May 1995).
Thomas J. Schaefer. The complexity of satisfiability problems. In Tenth Annual Symposium on Theory of Computing, 1978.
S. K. Shukla, D. J. Rosenkrantz, H. B. Hunt III, S. S. Ravi, and R. E. Stearns. A uniform approach for proving polynomial time decidability simulation relations for finite state processes. Research Report TR-95-6, Department of Computer Science, SUNY Albany, 1995.
L. J. Stockmeyer. Dexp-time hardness of bisimulation equivalence of concurrent system of finite state processes with hiding. (Unpublished Notes), 1992.
R.J. van Glabbeek. The linear time — branching time spectrum. Technical Report CS-R9029, Computer Science Department, CWI, Centre for Mathematics and Computer Science, Netherlands, 1990.
P. Wolper. Private communications. 1995.
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Shukla, S.K., Hunt, H.B., Rosenkrantz, D.J., Stearns, R.E. (1996). On the complexity of relational problems for finite state processes. In: Meyer, F., Monien, B. (eds) Automata, Languages and Programming. ICALP 1996. Lecture Notes in Computer Science, vol 1099. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61440-0_151
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DOI: https://doi.org/10.1007/3-540-61440-0_151
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