Abstract
We endow action sets of transition systems with a partial order that expresses the degree of specialization of actions, and with an intuitive but flexible consistency predicate that constrains the extension of such orders with more specialized actions. We develop a satisfaction relation for such models and theμ-calculus. We prove that this satisfaction relation is sound for Thomsen’s extended bisimulation as our refinement notion for models, even for consistent extensions of ordered action sets. We then demonstrate how this satisfaction relation can be reduced, fairly efficiently, to classical μ-calculus model checking. These results provide formal support for change management of models and their validation (e.g. in model-centric software development), and enable verification of concrete systems with respect to properties specified for abstract actions.
This work is in part financially supported by the DFG project (FE 942/2-1) and by the UK EPSRC project Complete and Efficient Checks for Branching-Time Abstractions EP/E028985/1.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Aceto, L.: Action refinement in process algebras. Cambridge University Press, Cambridge (1992)
Belnap, N.D.: A useful four-valued logic. In: Dunn, J.M., Epstein, G. (eds.) Modern Uses of Multiple-Valued Logic, pp. 8–37. D. Reidel, Dordrecht (1977)
Bruns, G., Godefroid, P.: Generalized Model Checking: Reasoning about Partial State Spaces. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, Springer, Heidelberg (2000)
Chechik, M., et al.: Multi-Valued Symbolic Model-Checking. ACM Transactions on Software Engineering and Methodology 12, 1–38 (2003)
Cousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: Proc.of POPL 1977, pp. 238–252. ACM Press, New York (1977)
Dams, D., Namjoshi, K.S.: The existence of finite abstractions for branching time model checking. In: Proc.of LICS 2004, pp. 335–344. IEEE Computer Society Press, Los Alamitos (2004)
Fecher, H., Huth, M.: Ranked Predicate Abstraction for Branching Time: Complete, Incremental, and Precise. In: Graf, S., Zhang, W. (eds.) ATVA 2006. LNCS, vol. 4218, pp. 322–336. Springer, Heidelberg (2006)
Fecher, H., et al.: Refinement sensitive formal semantics of state machines with persistent choice. In: Proc. of AVoCS 2007, ENCTS (to appear)
Glabbeek, R.v., Goltz, U.: Refinement of actions and equivalence notions for concurrent systems. Acta Informatica 37, 229–327 (2001)
Gorrieri, R., Rensink, A.: Action refinement. In: Bergstra, J.A., Ponse, A., Smolka, S.A. (eds.) Handbook of Process Algebra, pp. 1047–1147. North-Holland, Amsterdam (2001)
Huth, M.: Labelled transition systems as a Stone space. Logical Methods in Computer Science 1(1), 1–28 (2005)
Jurdzinski, M.: Deciding the winner in parity games is in UP ∩ co-UP. Inf. Process. Lett. 68(3), 119–124 (1998)
Kozen, D.: Results on the propositional μ-calculus. Theor. Comput. Sci. 27, 333–354 (1983)
Kupferman, O., Lustig, Y.: Lattice Automata. In: Cook, B., Podelski, A. (eds.) VMCAI 2007. LNCS, vol. 4349, pp. 199–213. Springer, Heidelberg (2007)
Kupferman, O., Lustig, Y.: Latticed Simulation Relations and Games. In: Namjoshi, K.S., et al. (eds.) ATVA 2007. LNCS, vol. 4762, pp. 316–330. Springer, Heidelberg (2007)
Lange, M., Stirling, C.: Model checking games for branching time logics. J. Log. Comput. 12(4), 623–639 (2002)
Larsen, K.G., Thomsen, B.: A modal process logic. In: Proc.of LICS 1988, pp. 203–210. IEEE Computer Society Press, Los Alamitos (1988)
Larsen, K.G., Xinxin, L.: Equation solving using modal transition systems. In: Proc. of LICS 1990, pp. 108–117. IEEE Computer Society Press, Los Alamitos (1990)
Lazic, R.: A semantic study of Data Independence with Applications to Model Checking, DPhil thesis, Oxford University Computing Laboratory (April 1999)
Milner, R.: A Calculus of Communication Systems. LNCS, vol. 92. Springer, Heidelberg (1980)
Park, D.: Concurrency and automata on infinite sequences. In: Deussen, P. (ed.) GI-TCS 1981. LNCS, vol. 104, pp. 167–183. Springer, Heidelberg (1981)
Plotkin, G., Stirling, C.: A framework for intuitionistic modal logics. In: Theoretical aspects of reasoning about knowledge, Monterey (1986)
Thomsen, B.: An extended bisimulation induced by a preorder on actions. Master’s thesis, Aalborg University Centre (1987)
Wilke, T.: Alternating tree automata, parity games, and modal μ-calculus. Bull. Soc. Math. Belg. 8, 359–391 (2001)
Zuck, L., Pnueli, A.: Model Checking and Abstraction to the Aid of Parameterized Systems (a survey). Computer Languages, Systems, and Structures 30(3-4), 139–169 (2004)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fecher, H., Huth, M. (2008). Model Checking for Action Abstraction. In: Logozzo, F., Peled, D.A., Zuck, L.D. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2008. Lecture Notes in Computer Science, vol 4905. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78163-9_13
Download citation
DOI: https://doi.org/10.1007/978-3-540-78163-9_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78162-2
Online ISBN: 978-3-540-78163-9
eBook Packages: Computer ScienceComputer Science (R0)