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Constructing Automata from Temporal Logic Formulas: A Tutorial⋆

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Lectures on Formal Methods and PerformanceAnalysis (EEF School 2000)

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Abstract

This paper presents a tutorial introduction to the construction of finite-automata on infinite words from linear-time temporal logic formulas. After defining the source and target formalisms, it describes a first construction whose correctness is quite direct to establish, but whose behavior is always equal to the worst-case upper bound. It then turns to the techniques that can be used to improve this algorithm in order to obtain the quite effective algorithms that are now in use.

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References

  1. J.R. Büchi. On a decision method in restricted second order arithmetic. In Proc. Internat. Congr. Logic, Method and Philos. Sci. 1960, pages 1–12, Stanford, 1962. Stanford University Press.

    Google Scholar 

  2. Orna Bernholtz, Moshe Y. Vardi, and Pierre Wolper. An automata-theoretic approach to branching-time model checking. In Computer Aided Verification, Proc. 6th Int. Workshop, volume 818 of Lecture Notes in Computer Science, pages 142–155, Stanford, California, June 1994. Springer-Verlag.

    Google Scholar 

  3. E.M. Clarke, E.A. Emerson, and A.P. Sistla. Automatic verification of finitestate concurrent systems using temporal logic specifications. ACM Transactions on Programming Languages and Systems, 8(2):244–263, January 1986.

    Article  MATH  Google Scholar 

  4. M. Daniele, F. Giunchiglia, and M.Y. Vardi. Improved automata generation for linear temporal logic. In Computer-Aided Verification, Proc. 11th Int. Conference, volume 633, pages 249–260, July 1999.

    Article  MathSciNet  Google Scholar 

  5. E.A. Emerson and E.M. Clarke. Using branching time logic to synthesize synchronization skeletons. Science of Computer Programming, 2:241–266, 1982.

    Article  MATH  Google Scholar 

  6. Rob Gerth, Doron Peled, Moshe Y. Vardi, and Pierre Wolper. Simple on-the-fly automatic verification of linear temporal logic. In Proc. 15th Work. Protocol Specification, Testing, and Verification, Warsaw, June 1995. North-Holland.

    Google Scholar 

  7. G. Holzmann. Design and Validation of Computer Protocols. Prentice-Hall International Editions, 1991.

    Google Scholar 

  8. Gerard J. Holzmann. The model checker SPIN. IEEE Transactions on Software Engineering, 23(5):279–295, May 1997. Special Issue: Formal Methods in Software Practice.

    Article  MathSciNet  Google Scholar 

  9. O. Kupferman and M. Vardi. iWeak alternating automata are not that weak. In Proc. 5th Israeli Symposium on Theory of Computing and Systems, pages 147–158. IEEE Computer Society Press, 1997.

    Google Scholar 

  10. Zohar Manna and Pierre Wolper. Synthesis of communicating processes from temporal logic specifications. ACM Transactions on Programming Languages and Systems, 6(1):68–93, January 1984.

    Article  MATH  Google Scholar 

  11. J.P. Queille and J. Sifakis. Specification and verification of concurrent systems in Cesar. In Proc. 5th Int’l Symp. on Programming, volume 137, pages 337–351. Springer-Verlag, Lecture Notes in Computer Science, 1981.

    Google Scholar 

  12. S. Safra. On the complexity of omega-automata. In Proceedings of the 29th IEEE Symposium on Foundations of Computer Science, White Plains, October 1988.

    Google Scholar 

  13. F. Somenzi and R. Bloem. Efficient büchi automata from ltl formulae. In Computer-Aided Verification, Proc. 12th Int. Conference, volume 1633, pages 247–263, 2000.

    Google Scholar 

  14. A. Prasad Sistla, Moshe Y. Vardi, and Pierre Wolper. The complementation problem for Büchi automata with applications to temporal logic. Theoretical Computer Science, 49:217–237, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  15. Wolfgang Thomas. Automata on infinite objects. In J. Van Leeuwen, editor, Handbook of Theoretical Computer Science-Volume B: Formal Models and Semantics, chapter 4, pages 133–191. Elsevier, Amsterdam, 1990.

    Google Scholar 

  16. Moshe Y. Vardi and Pierre Wolper. An automata-theoretic approach to automatic program verification. In Proceedings of the First Symposium on Logic in Computer Science, pages 322–331, Cambridge, June 1986.

    Google Scholar 

  17. Moshe Y. Vardi and Pierre Wolper. Reasoning about infinite computations. Information and Computation, 115(1):1–37, November 1994.

    Article  MATH  MathSciNet  Google Scholar 

  18. Pierre Wolper, Moshe Y. Vardi, and A. Prasad Sistla. Reasoning about infinite computation paths. In Proc. 24th IEEE Symposium on Foundations of Computer Science, pages 185–194, Tucson, 1983.

    Google Scholar 

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Wolper, P. (2001). Constructing Automata from Temporal Logic Formulas: A Tutorial⋆. In: Brinksma, E., Hermanns, H., Katoen, JP. (eds) Lectures on Formal Methods and PerformanceAnalysis. EEF School 2000. Lecture Notes in Computer Science, vol 2090. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44667-2_7

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  • DOI: https://doi.org/10.1007/3-540-44667-2_7

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  • Print ISBN: 978-3-540-42479-6

  • Online ISBN: 978-3-540-44667-5

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