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

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10119)


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



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.


  1. 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. 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 1991Google Scholar
  3. 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 MATHGoogle Scholar
  4. 4.
    Knapik, T., Niwiński, D., Urzyczyn, P.: Higher-order pushdown trees are easy. FoSSaCS 2002, 205–222 (2002)MathSciNetMATHGoogle Scholar
  5. 5.
    Kobayashi, N.: Model checking higher-order programs. J. ACM 60(3), 1–62 (2013)MathSciNetCrossRefMATHGoogle Scholar
  6. 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. 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. 8.
    Kupferman, O., Vardi, M.Y., Wolper, P.: An automata-theoretic approach to branching-time model checking. J. ACM 47(2), 312–360 (2000)MathSciNetCrossRefMATHGoogle Scholar
  9. 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. 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. 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 2011Google Scholar
  12. 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 2009Google Scholar
  13. 13.
    Platek, R.A.: Foundations of recursion theory. Ph.D. thesis, Standford University (1966)Google Scholar
  14. 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. 15.
    Scott, D.S.: A type-theoretical alternative to ISWIM, CUCH, OWHY. Theor. Comput. Sci. 121(1&2), 411–440 (1993)MathSciNetCrossRefMATHGoogle Scholar
  16. 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 CrossRefGoogle Scholar
  17. 17.
    Streett, R.S., Emerson, E.A.: An automata theoretic decision procedure for the propositional mu-calculus. Inf. Comput. 81(3), 249–264 (1989)MathSciNetCrossRefMATHGoogle Scholar
  18. 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. 19.
    Walukiewicz, I.: Pushdown processes: games and model-checking. Inf. Comput. 164(2), 234–263 (2001)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.University of OxfordOxfordUK

Personalised recommendations