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Axiomatising extended computation tree logic

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Trees in Algebra and Programming — CAAP '96 (CAAP 1996)

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Abstract

We present a sound and complete axiomatisation for extended computation tree logic. This language extends the standard computation tree logic CTL * by allowing path formulae to be expressed in linear time mu-calculus instead of linear time temporal logic. The main novelties in the current paper are an inference rule in the axiom system reflecting the limit closure of paths, a new strongly aconjunctive deterministic normal form for formulae, and the way the completeness proof takes advantage of techniques provided by automata theory.

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References

  1. Banieqbal, B. & Barringer, H.: Temporal logic with fixed points, in Temporal Logic in Specification, LNCS vol. 398, Springer-Verlag, 1989, pp. 62–74

    Google Scholar 

  2. Barringer, H. & Kuiper, R. & Pnueli, A.: A really abstract concurrent model and its temporal logic, in Proc. of the 13th ACM POPL, 1986

    Google Scholar 

  3. Clarke, E. & Grumberg, O. & Kurshan, R. P.: A synthesis of two approaches for verifying finite state concurrent systems, in Logic at Botik'89, LNCS vol. 363, Springer-Verlag, 1989, pp. 81–90

    Google Scholar 

  4. Emerson, E. A.: Alternative semantics for temporal logics, in Theoretical Computer Science, vol. 26, 1983, pp. 121–130

    Google Scholar 

  5. Emerson, E. A.: Temporal and modal logic, in van Leeuwen, J. (ed.): Handbook of Theoretical Computer Science, Elsevier/North-Holland, 1990, pp. 997–1072

    Google Scholar 

  6. Emerson, E. A. & Clarke, E. M.: Characterising correctness properties of parallel programs using fixpoints, in Proc. of the 7th ICALP, LNCS vol. 85, Springer-Verlag, 1980, pp. 169–181

    Google Scholar 

  7. Emerson, E. A. & Halpern, J. Y.: Decision procedures and expressiveness in the temporal logic of branching time, in Journal of Computer and System Sciences, vol. 30, 1985, pp. 1–24

    Google Scholar 

  8. Emerson, E. A. & Jutla, C. S.: Tree automata, mu-calculus, and determinacy, in Proceedings of the 32nd FOCS, 1991, pp. 368–377

    Google Scholar 

  9. Emerson, E. A. & Sistla, A. P.: Deciding full branching time logic, in Information and Control, vol. 61, pp. 175–201, 1984

    Google Scholar 

  10. Gabbay, D. & Pnueli, A. & Shelah, S. & Stavi, J.: On the temporal analysis of fairness, in Proc of the 7th ACM POPL, 1980, pp. 163–173

    Google Scholar 

  11. Kaivola, R.: Axiomatising linear time mu-calculus, in Proc. of CONCUR'95, LNCS vol. 962, Springer-Verlag, 1995, pp. 423–437

    Google Scholar 

  12. Kozen, D.: Results on the propositional Μ-calculus, in Theoretical Computer Science, vol. 27, 1983, pp. 333–354

    Google Scholar 

  13. Lichtenstein, O.: Decidability, Completeness, and Extensions of Linear Time Temporal Logic, PhD thesis, The Weizmann Institute of Science, Rehovot, Israel, 1991

    Google Scholar 

  14. McNaughton, R.: Testing and generating infinite sequences by a finite automaton, in Information and Control, vol. 9, 1966, pp. 521–530

    Google Scholar 

  15. Mostowski, A. W.: Hierarchies of weak automata and weak monadic formulas, in Theoretical Computer Science, vol. 83, 1991, pp. 232–335

    Google Scholar 

  16. Stirling, C.: Modal and temporal logics, in Abramsky, S. & al. (eds.): Handbook of Logic in Computer Science, Oxford University Press, 1992 pp. 477–563

    Google Scholar 

  17. Stirling, C. & Walker, D.: Local model checking in the modal mu-calculus, in Theoretical Computer Science, vol. 89, 1991, pp. 161–177

    Google Scholar 

  18. Streett, R. S. & Emerson, E. A.: An automata theoretic decision procedure for the propositional mu-calculus, in Inf. and Comp., vol. 81, 1989, pp. 249–264

    Google Scholar 

  19. Thomas, W.: Computation tree logic and regular Ω-languages, in Linear Time, Branching Time and Partial Order in Concurrency, LNCS vol. 354, Springer-Verlag, 1988, pp. 690–713

    Google Scholar 

  20. Thomas, W.: Automata on infinite objects, in van Leeuwen, J. (ed.): Handbook of Theoretical Computer Science, vol. 2, North-Holland, 1989, pp. 133–191

    Google Scholar 

  21. Vardi, M. Y.: A temporal fixpoint calculus, in Proceedings of the 15th ACM POPL, 1988, pp. 250–259

    Google Scholar 

  22. Vardi, M. Y. & Wolper, P.: Yet another process logic, in Logics of Programs, LNCS vol. 164, Springer-Verlag, 1983, pp. 501–512

    Google Scholar 

  23. Vardi, M. Y. & Wolper, P.: Reasoning about infinite computations, in Information and Computation, vol. 115, 1994, pp. 1–37

    Google Scholar 

  24. Walukiewicz, I.: Completeness of Kozen's axiomatisation of the propositional Μ-calculus, in Proc. of the 10th IEEE LICS, 1995

    Google Scholar 

  25. Wolper, P.: Temporal logic can be more expressive, in Information and Control, vol 56, 1983, pp. 72–99

    Google Scholar 

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Authors and Affiliations

  1. Laboratory for Foundations of Computer Science, University of Edinburgh, The King's Buildings, EH9 3JZ, Edinburgh, UK

    Roope Kaivola

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  1. Roope Kaivola
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Hélène Kirchner

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© 1996 Springer-Verlag Berlin Heidelberg

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Kaivola, R. (1996). Axiomatising extended computation tree logic. In: Kirchner, H. (eds) Trees in Algebra and Programming — CAAP '96. CAAP 1996. Lecture Notes in Computer Science, vol 1059. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61064-2_31

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  • DOI: https://doi.org/10.1007/3-540-61064-2_31

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61064-9

  • Online ISBN: 978-3-540-49944-2

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