Abstract
We propose the use of tree automata as abstractions in the verification of branching time properties, and show several benefits. In this setting, soundness and completeness are trivial. It unifies the abundance of frameworks in the literature, and clarifies the role of concepts therein in terms of the well-studied field of automata theory. Moreover, using automata as models simplifies and generalizes results on maximal model theorems.
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Bruns, G., Godefroid, P.: Model checking partial state spaces with 3-valued temporal logics. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, pp. 274–287. Springer, Heidelberg (1999)
Chechik, M., Easterbrook, S., Petrovykh, V.: Model-Checking over Multi-valued Logics. In: Oliveira, J.N., Zave, P. (eds.) FME 2001. LNCS, vol. 2021, p. 72. Springer, Heidelberg (2001)
Clarke, E.M., Emerson, E.A.: Design and synthesis of synchronization skeletons using branching time temporal logic. In: Kozen, D. (ed.) Logic of Programs 1981. LNCS, vol. 131. Springer, Heidelberg (1981)
Cleaveland, R., Iyer, P., Yankelevich, D.: Optimality in abstractions of model checking. In: Mycroft, A. (ed.) SAS 1995. LNCS, vol. 983. Springer, Heidelberg (1995)
Cousot, P., Cousot, R.: Abstract interpretation: A unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: POPL (1977)
Dams, D., Namjoshi, K.S.: The existence of finite abstractions for branching time model checking. In: LICS (2004)
Dams, D., Gerth, R., Grumberg, O.: Abstract interpretation of reactive systems. ACM TOPLAS 19(2), 253–291 (1997)
Dams, D., Lakhnech, Y., Steffen, M.: Iterating transducers. J. of Logic and Algebraic Programming, 52–53, 109–127 (2002)
Dams, D.: Abstract Interpretation and Partition Refinement for Model Checking. PhD thesis (July 1996)
de Alfaro, L., Godefroid, P., Jagadeesan, R.: Three-valued abstractions of games: Uncertainty, but with precision. In: LICS (2004)
Emerson, E.A., Jutla, C.S.: The complexity of tree automata and logics of programs (extended abstract). In: FOCS (1988); Full version in SIAM Journal of Computing, 29(1), 132–158 (1999)
Emerson, E.A., Jutla, C.S.: Tree automata, mu-calculus and determinacy (extended abstract). In: FOCS (1991)
Godefroid, P., Jagadeesan, R.: On the expressiveness of 3-valued models. In: Zuck, L.D., Attie, P.C., Cortesi, A., Mukhopadhyay, S. (eds.) VMCAI 2003. LNCS, vol. 2575, pp. 206–222. Springer, Heidelberg (2002)
Giacobazzi, R., Ranzato, F., Scozzari, F.: Making abstract interpretations complete. Journal of the ACM 47(2), 361–416 (2000)
Grumberg, O., Long, D.E.: Model checking and modular verification. In: ACM TOPLAS (1994)
Henzinger, T.A., Kupferman, O., Rajamani, S.: Fair simulation. In: Mazurkiewicz, A., Winkowski, J. (eds.) CONCUR 1997. LNCS, vol. 1243. Springer, Heidelberg (1997)
Huth, M., Jagadeesan, R., Schmidt, D.: Modal transition systems: A foundation for three-valued program analysis. In: Sands, D. (ed.) ESOP 2001. LNCS, vol. 2028, p. 155. Springer, Heidelberg (2001)
Janin, D., Walukiewicz, I.: Automata for the modal mu-calulus and related results. In: Hájek, P., Wiedermann, J. (eds.) MFCS 1995. LNCS, vol. 969. Springer, Heidelberg (1995)
Janin, D., Walukiewicz, I.: On the expressive completeness of the propositional mu-calculus with respect to monadic second order logic. In: Sassone, V., Montanari, U. (eds.) CONCUR 1996. LNCS, vol. 1119. Springer, Heidelberg (1996)
Kesten, Y., Pnueli, A.: Verification by augmented finitary abstraction. Information and Computation 163(1), 203–243 (2000)
Kupferman, O., Vardi, M.Y.: Modular model checking. In: de Roever, W.-P., Langmaack, H., Pnueli, A. (eds.) COMPOS 1997. LNCS, vol. 1536, p. 381. Springer, Heidelberg (1998)
Larsen, K.G., Thomsen, B.: A modal process logic. In: LICS (1988)
Larsen, K.G., Xinxin, L.: Equation solving using modal transition systems. In: LICS (1990)
Milner, R.: An algebraic definition of simulation between programs. In: 2nd IJCAI. William Kaufmann, San Francisco (1971)
Namjoshi, K.S.: Abstraction for branching time properties. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 288–300. Springer, Heidelberg (2003)
Nielson, F., Nielson, H.R., Hankin, C.: Principles of Program Analysis. Springer, Heidelberg (1999)
Queille, J.P., Sifakis, J.: Specification and verification of concurrent systems in CESAR. In: Dezani-Ciancaglini, M., Montanari, U. (eds.) Programming 1982. LNCS, vol. 137. Springer, Heidelberg (1982)
Schmidt, D.A.: Closed and logical relations for over- and under-approximation of powersets. In: Giacobazzi, R. (ed.) SAS 2004. LNCS, vol. 3148, pp. 22–37. Springer, Heidelberg (2004)
Seidl, H.: Deciding equivalence of finite tree automata. SIAM Journal of Computing 19, 424–437 (1990)
Shoham, S., Grumberg, O.: Monotonic abstraction-refinement for CTL. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 546–560. Springer, Heidelberg (2004)
Streett, R.S., Emerson, E.A.: The propositional mu-calculus is elementary. In: Paredaens, J. (ed.) ICALP 1984. LNCS, vol. 172. Springer, Heidelberg (1984), pp. 249–264. Springer, Heidelberg (1984); Full version in information and computation 81(3), 249–264 (1989)
Uribe, T.E.: Abstraction-Based Deductive-Algorithmic Verification of Reactive Systems. PhD thesis, Stanford University (1999)
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Dams, D., Namjoshi, K.S. (2005). Automata as Abstractions. In: Cousot, R. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2005. Lecture Notes in Computer Science, vol 3385. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30579-8_15
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DOI: https://doi.org/10.1007/978-3-540-30579-8_15
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