TCS 2012: Theoretical Computer Science pp 250-264 | Cite as
Unique Parallel Decomposition in Branching and Weak Bisimulation Semantics
Conference paper
Abstract
We consider the property of unique parallel decomposition modulo branching and weak bisimilarity. First, we show that totally normed behaviours always have parallel decompositions, but that these are not necessarily unique. Then, we establish that finite behaviours have unique parallel decompositions. We derive the latter result from a general theorem about unique decompositions in partial commutative monoids.
Keywords
Operational Semantic Parallel Composition Process Expression Unique Decomposition Commutative Monoids
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.
Download
to read the full conference paper text
References
- 1.Aceto, L., Fokkink, W.J., Ingólfsdóttir, A., Luttik, B.: A finite equational base for CCS with left merge and communication merge. ACM Trans. Comput. Log. 10(1) (2009)Google Scholar
- 2.Balabonski, T., Haucourt, E.: A Geometric Approach to the Problem of Unique Decomposition of Processes. In: Gastin, P., Laroussinie, F. (eds.) CONCUR 2010. LNCS, vol. 6269, pp. 132–146. Springer, Heidelberg (2010)CrossRefGoogle Scholar
- 3.Basten, T.: Branching bisimilarity is an equivalence indeed? Information Processing Letters 58(3), 141–147 (1996)MathSciNetMATHCrossRefGoogle Scholar
- 4.Castellani, I., Hennessy, M.: Distributed bisimulations. J. ACM 36(4), 887–911 (1989)MathSciNetMATHCrossRefGoogle Scholar
- 5.Christensen, S.: Decidability and Decomposition in Process Algebras. PhD thesis, University of Edinburgh (1993)Google Scholar
- 6.Corradini, F., Gorrieri, R., Marchignoli, D.: Towards parallelization of concurrent systems. RAIRO Inform. Théor. Appl. 32(4-6), 99–125 (1998)MathSciNetGoogle Scholar
- 7.Dreier, J., Ene, C., Lafourcade, P., Lakhnech, Y.: On unique decomposition of processes in the applied π-calculus. Technical Report TR-2012-3, Verimag Research Report (2011)Google Scholar
- 8.Fokkink, W.J., Luttik, S.P.: An ω-Complete Equational Specification of Interleaving. In: Welzl, E., Montanari, U., Rolim, J.D.P. (eds.) ICALP 2000. LNCS, vol. 1853, pp. 729–743. Springer, Heidelberg (2000)CrossRefGoogle Scholar
- 9.Fröschle, S., Lasota, S.: Normed processes, unique decomposition, and complexity of bisimulation equivalences. ENTCS 239, 17–42 (2009)Google Scholar
- 10.van Glabbeek, R.J., Weijland, W.P.: Branching time and abstraction in bisimulation semantics. J. ACM 43(3), 555–600 (1996)MathSciNetMATHCrossRefGoogle Scholar
- 11.Groote, J.F., Moller, F.: Verification of Parallel Systems Via Decomposition. In: Cleaveland, W.R. (ed.) CONCUR 1992. LNCS, vol. 630, pp. 62–76. Springer, Heidelberg (1992)CrossRefGoogle Scholar
- 12.Hirshfeld, Y., Jerrum, M.: Bisimulation Equivalence is Decidable for Normed Process Algebra. In: Wiedermann, J., Van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, pp. 412–421. Springer, Heidelberg (1999)CrossRefGoogle Scholar
- 13.Kleene, S.C.: Introduction to Metamathematics. D. Van Nostrand Co., Inc., New York (1952)Google Scholar
- 14.Luttik, B.: Unique parallel decomposition in branching and weak bisimulation semantics. CoRR, abs/1205.2117 (2012)Google Scholar
- 15.Luttik, B., van Oostrom, V.: Decomposition orders—another generalisation of the fundamental theorem of arithmetic. Theor. Comput. Sci. 335(2-3), 147–186 (2005)MATHCrossRefGoogle Scholar
- 16.Milner, R.: Communication and Concurrency. Prentice-Hall International (1989)Google Scholar
- 17.Milner, R.: Operational and algebraic semantics of concurrent processes. In: Handbook of Theoretical Computer Science, vol. B: Formal Models and Semantics (B), pp. 1201–1242. The MIT Press (1990)Google Scholar
- 18.Milner, R., Moller, F.: Unique decomposition of processes. Theoret. Comput. Sci. 107, 357–363 (1993)MathSciNetMATHCrossRefGoogle Scholar
- 19.Moller, F.: Axioms for Concurrency. PhD thesis, University of Edinburgh (1989)Google Scholar
- 20.Moller, F.: The Importance of the Left Merge Operator in Process Algebras. In: Paterson, M. (ed.) ICALP 1990. LNCS, vol. 443, pp. 752–764. Springer, Heidelberg (1990)CrossRefGoogle Scholar
- 21.Moller, F.: The nonexistence of finite axiomatisations for CCS congruences. In: Proceedings of LICS 1990, pp. 142–153. IEEE Computer Society (1990)Google Scholar
Copyright information
© IFIP International Federation for Information Processing 2012