Abstract
Recently, Milner and Moller have presented several decomposition results for processes. Inspired by these, we investigate decomposition techniques for the verification of parallel systems. In particular, we consider those of the form p 1∥p 2∥ ...∥p m = q 1 ∥q 2 ∥...∥q n (*) where p iand q j are (finite-) state systems, and ∥denotes parallel composition. We provide a decomposition procedure for all p i and q j and give criteria that must be checked on the decomposed processes to see whether (*) does or does not hold. We analyse the complexity of our procedure and show that it is polynomial in n, m and the sizes of p i and q j if there is no communication. We also show that with communication the verification of (*) is co-NP hard, which makes it very unlikely that a polynomial complexity bound exists. But by applying our decomposition technique to Milner's cyclic scheduler we show that verification can become polynomial in space and time for practical examples, where standard techniques are exponential.
Research supported by ESPRIT BRA Grant No. 3006 - CONCUR
Preview
Unable to display preview. Download preview PDF.
References
J.C.M. Baeten and W.P. Weijland. Process Algebra. Cambridge Tracts in Theoretical Computer Science 18. Cambridge University Press, 1990.
A. Bouajjani, J.-C. Fernandez and N. Halbwachs. Minimal model generation. Draft, 1991.
J.R. Burch, E.M. Clarke, K.L. McMillan, D.L. Dill, and L.J. Hwang. Symbolic model checking 1020 states and beyond. In Proceedings 5 th Annual Symposium on Logic in Computer Science, Philadelphia, USA, pages 428–439, 1990.
S.A. Cook. The complexity of theorem-proving procedures. In Proceedings of the 3 rd Annual ACM Symposium on Theory of Computing, Shaker Heights, Ohio, pages 151–158, 1971.
J. Engelfriet. Determinacy → (observation equivalence = trace equivalence). Theoretical Computer Science, 36(1):21–25, 1985.
J.-C. Fernandez. An implementation of an efficient algorithm for bisimulation equivalence. Science of Computer Programming, 13:219–236, 1989/1990.
J.-C. Fernandez and L. Mounier. “On the fly” verification of behavioural equivalences and preorders. In K.G. Larsen, editors, Proceedings CAV'91, Aalborg, pages 238–250. 1991.
R.J. van Glabbeek. The linear time — branching time spectrum. In J.C.M. Baeten and J.W. Klop, editors, Proceedings CONCUR '90, Amsterdam, volume 458 of Lecture Notes in Computer Science, pages 278–297. Springer-Verlag, 1990.
J.F. Groote and F.W. Vaandrager. Structured operational semantics and bisimulation as a congruence (extended abstract). In G. Ausiello, M. Dezani-Ciancaglini, and S. Ronchi Della Rocca, editors, Proceedings 16 th ICALP, Stresa, volume 372 of Lecture Notes in Computer Science, pages 423–438. Springer-Verlag, 1989. Full version to appear in Information and Computation.
J.F. Groote and F.W. Vaandrager. An efficient algorithm for branching bisimulation and stuttering equivalence. In M.S. Paterson, editor, Proceedings 17 th ICALP, Warwick, volume 443 of Lecture Notes in Computer Science, pages 626–638. Springer-Verlag, 1990.
C.A.R. Hoare. Communicating Sequential Processes. Prentice-Hall International, 1985.
G.J. Holzmann. Design and Validation of Computer Protocols. Prentice-Hall International, 1991.
H. Qin. Efficient verification of determinate processes. In J.C.M. Baeten and J.F. Groote, editors, Proceedings CONCUR'91, Amsterdam, volume 527 of Lecture Notes in Computer Science, pages 471–494. Springer-Verlag, 1991.
P.C. Kanellakis and S.A. Smolka. CCS expressions, finite-state processes, and three problems of equivalence. Information and Compulation, 86:43–68, 1990.
R. Milner. A Calculus of Communicating Systems, volume 92 of Lecture Notes in Computer Science. Springer-Verlag, 1980.
R. Milner. Communication and Concurrency. Prentice-Hall International, 1989.
R. Milner and F. Moller. Unique decomposition of processes. Bulletin of the European Association for Theoretical Computer Science, 41:226–232, 1990.
F. Moller. Axioms for concurrency. PhD thesis, Report CST-59-89, Department of Computer Science, University of Edinburgh, 1989.
A. Rabinovich. Checking equivalences between concurrent systems of finite agents. Draft, 1991.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Groote, J.F., Moller, F. (1992). Verification of parallel systems via decomposition. In: Cleaveland, W. (eds) CONCUR '92. CONCUR 1992. Lecture Notes in Computer Science, vol 630. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0084783
Download citation
DOI: https://doi.org/10.1007/BFb0084783
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55822-4
Online ISBN: 978-3-540-47293-3
eBook Packages: Springer Book Archive