Abstract
We have been studying abstractions of linked structures, in which cells are connected by pointers, using temporal logic. This paper presents some our results for these abstractions. The system to be verified is a transition system on a graph. The shape of the graph does not change as a result of the transition, but the label assigned to each cell (node) changes according to rewrite rules. The labels of cells are changed synchronously or asynchronously. We abstract such systems using abstract cells and abstract graphs. Abstract cells are characterized by a set of temporal formulas, and different abstractions can be tried by changing the set of formulas. Some examples of analysis are also described.
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References
Takahashi, K., Hagiya, M.: Abstraction of link structures by regular expressions and abstract model checking of concurrent garbage collection. In: First Asian Workshop on Programming Languages and Systems, National University of Singapore, pp. 1–8 (2000), http://nicosia.is.s.u-tokyo.ac.jp/members/hagiya.html
Takahashi, K., Hagiya, M.: Formal proof of abstract model checking of concurrent garbage collection. In: Kamareddine, F. (ed.) Workshop on Thirty Five years of Automath, Informal Proceedings, Heriot-Watt University, pp. 115–126 (2002), http://nicosia.is.s.u-tokyo.ac.jp/members/hagiya.html
Takahashi, K., Hagiya, M.: Abstraction of graph transformation using temporal formulas. In: Workshop on Model-Checking for Dependable Software-Intensive Systems, International Conference on Dependable Systems and Networks, DSN 2003 (2003), http://nicosia.is.s.u-tokyo.ac.jp/members/hagiya.html
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, pp. 52–71. Springer, Heidelberg (1982)
Emerson, E.A., Clarke, E.M.: Characterizing correctness properties of parallel programs using fixpoints. In: de Bakker, J.W., van Leeuwen, J. (eds.) ICALP 1980. LNCS, vol. 85, pp. 169–180. Springer, Heidelberg (1980)
Graf, S., Saidi, H.: Construction of abstract state graphs with PVS. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 72–83. Springer, Heidelberg (1997)
Henzinger, T.A., Jhala, R., Majumdar, R., Sutre, G.: Lazy abstraction. In: Symposium on Principles of Programming Languages, pp. 58–70 (2002)
Vardi, M.Y.: Reasoning about the past with two-way automata. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 628–641. Springer, Heidelberg (1998)
von Neumann, J.: Theory of Self-Reproducing Automata. University of Illinois Press, Urbana (1966)
Wolfram, S.: Cellular Automata and Complexity. Addison-Wesley, Reading (1994)
Kozen, D., Tiuryn, J.: Logic of programs. In: Formal Models and Sematics, Handbook of Theoretical Computer Science, vol. B, pp. 789–840. Elsevier Science Publishers, Amsterdam (1990)
Andréka, H., Németi, I., van Benthem, J.: Modal languages and bounded fragments of predicate logic. Journal of Philosophical Logic 27, 217–274 (1998)
Alur, R., Courcoubetis, C., Dill, D.: Model checking for real-time systems. In: Proceedings of the Fifth Annual Symposium on Logic in Computer Science, pp. 414–425. IEEE Computer Society Press, Los Alamitos (1990)
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Hagiya, M., Takahashi, K., Yamamoto, M., Sato, T. (2004). Analysis of Synchronous and Asynchronous Cellular Automata Using Abstraction by Temporal Logic. In: Kameyama, Y., Stuckey, P.J. (eds) Functional and Logic Programming. FLOPS 2004. Lecture Notes in Computer Science, vol 2998. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24754-8_2
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DOI: https://doi.org/10.1007/978-3-540-24754-8_2
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