Generic Forward and Backward Simulations
The technique of forward/backward simulations has been applied successfully in many distributed and concurrent applications. In this paper, however, we claim that the technique can actually have more genericity and mathematical clarity. We do so by identifying forward/backward simulations as lax/oplax morphisms of coalgebras. Starting from this observation, we present a systematic study of this generic notion of simulations. It is meant to be a generic version of the study by Lynch and Vaandrager, covering both non-deterministic and probabilistic systems. In particular we prove soundness and completeness results with respect to trace inclusion: the proof is by coinduction using the generic theory of traces developed by Jacobs, Sokolova and the author. By suitably instantiating our generic framework, one obtains the appropriate definition of forward/backward simulations for various kinds of systems, for which soundness and completeness come for free.
KeywordsStart State Forward Simulation Shapely Functor Probabilistic Automaton Trace Semantic
Unable to display preview. Download preview PDF.
- 1.Cheung, L.: Reconciling Nondeterministic and Probabilistic Choices. PhD thesis, Radboud Univ. Nijmegen (2006)Google Scholar
- 3.Garland, S., Lynch, N., Vaziri, M.: IOA: a language for specifying, programming, and validating distributed systems. MIT Laboratory for Computer Science, Cambridge (1997)Google Scholar
- 5.Hasuo, I., Jacobs, B., Sokolova, A.: Generic trace theory. In: Coalgebraic Methods in Computer Science (CMCS 2006). Elect. Notes in Theor. Comp. Sci. Elsevier, Amsterdam (2006)Google Scholar
- 6.Hasuo, I.: Generic forward and backward simulations. Technical report, Research Center for Verification and Semantics, National Institute of Advanced Industrial Science and Technology (AIST), Japan (2006), http://www.cs.ru.nl/ichiro/papers/
- 8.Jou, C., Smolka, S.: Equivalences, congruences and complete axiomatizations for probabilistic processes. In: Baeten, J.C.M., Klop, J.W. (eds.) CONCUR 1990. LNCS, vol. 458, pp. 367–383. Springer, Heidelberg (1990)Google Scholar
- 9.Kawabe, Y., Mano, K., Sakurada, H., Tsukada, Y.: Backward simulations for anonymity. In: International Workshop on Issues in the Theory of Security (WITS 2006) (2006)Google Scholar
- 11.Klarlund, N., Schneider, F.: Verifying safety properties using infinite-state automata. Technical Report 89-1039, Department of Computer Science, Cornell University, Ithaca, New York (1989)Google Scholar
- 13.Power, J., Turi, D.: A coalgebraic foundation for linear time semantics. In: Category Theory and Computer Science. Elect. Notes in Theor. Comp. Sci, vol. 29. Elsevier, Amsterdam (1999)Google Scholar
- 16.Sokolova, A.: Coalgebraic Analysis of Probabilistic Systems. PhD thesis, TU Eindhoven (2005)Google Scholar