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Automata, Logic and Games for the \(\lambda \)-Calculus

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Logic and Its Applications (ICLA 2017)

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Abstract

Automata, logic and games provide the mathematical theory that underpins the model checking of reactive systems.

Abstract of an invited talk presented at ICLA 2017.

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Notes

  1. 1.

    We suppress a delicate distinction between types and a subsystem of parity permissive types. There is a corresponding distinction between ADTA and a subclass of parity permissive ADTA. The expressive equivalence result holds both generally and when restricted to the parity permissive subsystems.

References

  1. Clairambault, P., Murawski, A.S.: Böhm trees as higher-order recursive schemes. In: Proceedings of IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013), LIPIcs, vol. 24, pp. 91–102. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2013)

    Google Scholar 

  2. Emerson, E.A., Jutla, C.S.: Tree automata, mu-calculus and determinacy (extended abstract). In: 32nd Annual Symposium on Foundations of Computer Science, San Juan, Puerto Rico, vol. 1–4 , pp. 368–377, October 1991

    Google Scholar 

  3. Grädel, E., Thomas, W., Wilke, T. (eds.): Automata, Logics, and Infinite Games: A Guide to Current Research. LNCS, vol. 2500. Springer, Heidelberg (2002). doi:10.1007/3-540-36387-4

    MATH  Google Scholar 

  4. Knapik, T., Niwiński, D., Urzyczyn, P.: Higher-order pushdown trees are easy. FoSSaCS 2002, 205–222 (2002)

    MathSciNet  MATH  Google Scholar 

  5. Kobayashi, N.: Model checking higher-order programs. J. ACM 60(3), 1–62 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  6. Kobayashi, N., Ong, C.-H.L.: A type system equivalent to the modal mu-calculus model checking of higher-order recursion schemes. In: Proceedings of the 24th Annual IEEE Symposium on Logic in Computer Science, LICS 2009, 11–14 August 2009, Los Angeles, CA, USA, pp. 179–188 (2009)

    Google Scholar 

  7. Kobayashi, N., Sato, R., Unno, H.: Predicate abstraction and CEGAR for higher-order model checking. In: Hall, M.W., Padua, D.A. (eds.) PLDI, pp. 222–233. ACM (2011)

    Google Scholar 

  8. Kupferman, O., Vardi, M.Y., Wolper, P.: An automata-theoretic approach to branching-time model checking. J. ACM 47(2), 312–360 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  9. Ong, C.-H.L.: On model-checking trees generated by higher-order recursion schemes. In: Proceedings of 21th IEEE Symposium on Logic in Computer Science (LICS 2006), pp. 81–90. IEEE Computer Society (2006)

    Google Scholar 

  10. Ong, C.-H.L.: Higher-order model checking: an overview. In: 30th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2015, Kyoto, Japan, 6–10 July 2015, pp. 1–15 (2015)

    Google Scholar 

  11. Ong, C.-H.L., Ramsay, S.J.: Verifying higher-order functional programs with pattern-matching algebraic data types. In: POPL 2011, vol. 46, pp. 587–598, January 2011

    Google Scholar 

  12. Ong, C.-H.L., Tzevelekos, N.: Functional reachability. In: 2009 24th Annual IEEE Symposium on Logic in Computer Science (LICS 2009), pp. 286–295, August 2009

    Google Scholar 

  13. Platek, R.A.: Foundations of recursion theory. Ph.D. thesis, Standford University (1966)

    Google Scholar 

  14. Ramsay, S.J., Neatherway, R.P., Ong, C.-H.L.: A type-directed abstraction refinement approach to higher-order model checking. In: The 41st Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 2014, San Diego, CA, USA, 20–21 January 2014, pp. 61–72. ACM (2014)

    Google Scholar 

  15. Scott, D.S.: A type-theoretical alternative to ISWIM, CUCH, OWHY. Theor. Comput. Sci. 121(1&2), 411–440 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  16. Stirling, C.: Dependency tree automata. In: Alfaro, L. (ed.) FoSSaCS 2009. LNCS, vol. 5504, pp. 92–106. Springer, Heidelberg (2009). doi:10.1007/978-3-642-00596-1_8

    Chapter  Google Scholar 

  17. Streett, R.S., Emerson, E.A.: An automata theoretic decision procedure for the propositional mu-calculus. Inf. Comput. 81(3), 249–264 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  18. Tsukada, T., Ong, C.-H.L.: Compositional higher-order model checking via \(\omega \)-regular games over böhm trees. In: Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), CSL-LICS 2014, Vienna, Austria, 14–18 July 2014, pp. 78:1–78:10 (2014)

    Google Scholar 

  19. Walukiewicz, I.: Pushdown processes: games and model-checking. Inf. Comput. 164(2), 234–263 (2001)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This is based on joint work with Matthew Hague, Steven Ramsay, and Takeshi Tsukada, partially funded by EPSRC UK. Part of the work was done while the authors were visiting the Institute for Mathematical Sciences, National University of Singapore in 2016. The visit was partially supported by the Institute.

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Correspondence to C.-H. Luke Ong .

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Ong, CH.L. (2017). Automata, Logic and Games for the \(\lambda \)-Calculus. In: Ghosh, S., Prasad, S. (eds) Logic and Its Applications. ICLA 2017. Lecture Notes in Computer Science(), vol 10119. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-54069-5_3

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  • DOI: https://doi.org/10.1007/978-3-662-54069-5_3

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