Abstract
A syntax directed mapping is presented from Propositional Temporal Logic (PTL) formulae to Müller type finite automata. This is a direct and much more elegant and easier to implement approach than previously described methods. Most of these methods are based on tableau methods for satisfiability checking, and after that a Büchi type of automaton is extracted. Büchi and Müller automata are equally expressive. However, Müller automata have nicer properties than Büchi automata, for instance deterministic Müller automata are expressive as non-deterministic ones, while this is not true for Büchi automata. Also deterministic Büchi automata are not closed under complement. This transformation is the first step in a decision procedure, since the resulting Müller automaton represents the models of the temporal logic formula, and on which further verification and analysis can be performed.
This research is part of the ASCIS project sponsored by the European Community under contract BRA 3281.
Chapter PDF
Similar content being viewed by others
Keywords
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.
References
PNUELI, A., “Applications of Temporal Logic to the Specification and Verification of Reactive Systems: A Survey of Current Trends,” Current Trends in Concurrency: Overviews and Tutorials, ed. J. W. de Bakker, W.-P. de Roever and G. Rozenberg, Lecture Notes in Computer Science 224, Springer Verlag, Berlin, pp. 510–584.
v. BOCHMANN, G., “Hardware Specification with Temporal Logic: An Example,” IEEE Trans. on Computers, vol. C-31, no. 3, March 1982, pp. 223–231.
JANSSEN, G. L. J. M., “Hardware verification using Temporal Logic: A Practical View,” Formal VLSI Correctness Verification, VLSI Design Methods-II, Proc. of the IMEC-IFIP WG10.2 WG 10.5 International Workshop on Applied Formal Methods for Correct VLSI Design, ed. L. J. M. Claesen, North-Holland, 1990, pp. 159–168.
WOLPER, P., “Temporal Logic Can Be More Expressive,” Information and Control, vol. 56, 1983, pp. 72–99.
WOLPER, P., M. Y. VARDI, and A. P. SISTLA, “Reasoning about Infinite Computation Paths,” Proc. 24th Ann. Symp. on Foundations of Computer Science, Tucson, AZ, November 7–9,1983, pp. 185–193.
MANNA, Z. and A. PNUELI, “Specification and Verification of Concurrent Programs by ∀-Automata,” Proc. 14th ACM Symp. on Principles of Programming Languages, Munich, January 21–23, 1987, pp. 1–12.
ALPERN, B. and F. B. SCHNEIDER, ‘Verifying Temporal Properties without Temporal Logic,” ACM Trans. on Programming Languages and Systems, vol. 11, no. 1, January 1989, pp. 147–167.
CHOUEKA, Y., “Theories of Automata on Ω-Tapes: a Simplified Approach,” J. Comput. System Sci., vol. 8, 1974, pp. 117–141.
SISTLA, A. P., M. Y. VARDI, and P. WOLPER, “The Complementation Problems for Büchi Automata with Applications to Temporal Logic,” Proc. 12th Int. Colloquium on Automata, Languages and Programming (ICALP'85), Lecture Notes in Computer Science 194, Springer Verlag, Berlin, Napflion, Greece, July 1985, pp. 465–474.
RABIN, M. O. and D. SCOTT, “Finite Automata and their Decision Problems,” IBM J. Res. Develop., vol. 3, 1959, pp. 114–125.
McNAUGHTON, R., “Testing an Generating Infinite Sequences by a Finite Automaton,” Information and Control, vol. 9, 1966, pp. 521–530.
LICHTENSTEIN, O. and A. PNUELI, “Checking That Finite State Concurrent Programs Satisfy Their Linear Specification,” Proc. 12th ACM Symp. on Principles of Programming Languages, New Orleans, January 14–16, 1985, pp. 97–107.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
de Jong, G.G. (1992). An automata theoretic approach to Temporal Logic. In: Larsen, K.G., Skou, A. (eds) Computer Aided Verification. CAV 1991. Lecture Notes in Computer Science, vol 575. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55179-4_44
Download citation
DOI: https://doi.org/10.1007/3-540-55179-4_44
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55179-9
Online ISBN: 978-3-540-46763-2
eBook Packages: Springer Book Archive