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