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Finitary Semantics of Linear Logic and Higher-Order Model-Checking

  • Charles GrelloisEmail author
  • Paul-André MellièsEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9234)

Abstract

In this paper, we explain how the connection between higher-order model-checking and linear logic recently exhibited by the authors leads to a new and conceptually enlightening proof of the selection problem originally established by Carayol and Serre using collapsible pushdown automata. The main idea is to start from an infinitary and colored relational semantics of the \(\lambda \,Y\)-calculus formulated in a companion paper, and to replace it by a finitary counterpart based on finite prime-algebraic lattices. Given a higher-order recursion scheme \(\mathcal {G}\), the finiteness of its interpretation in the resulting model enables us to associate to any MSO formula \(\varphi \) a higher-order recursion scheme \(\mathcal {G}_{\varphi }\) resolving the selection problem.

Keywords

Higher-order model-checking Linear logic Selection problem Finitary semantics Parity games 

References

  1. 1.
    Bloom, S.L., Ésik, Z.: Fixed-point operations on CCC’s. Part I. Theor. Comput. Sci. 155(1), 1–38 (1996)CrossRefzbMATHGoogle Scholar
  2. 2.
    Carayol, A., Serre, O.: Collapsible pushdown automata and labeled recursion schemes: equivalence, safety and effective selection. In: LICS 2012. pp. 165–174. IEEE Computer Society (2012)Google Scholar
  3. 3.
    Coppo, M., Dezani-Ciancaglini, M., Honsell, F., Longo, G.: Extended Type Structures and Filter Lambda Models. In: Lolli, G., Longo, G., Marcja, A. (eds.) Logic Colloquium 82, pp. 241–262. North-Holland, Amsterdam (1984)CrossRefGoogle Scholar
  4. 4.
    Grellois, C., Melliès, P.-A.: An infinitary model of linear logic. In: Pitts, A. (ed.) FOSSACS 2015. LNCS, vol. 9034, pp. 41–55. Springer, Heidelberg (2015) CrossRefGoogle Scholar
  5. 5.
    Grellois, C., Melliès, P.A.: Relational semantics of linear logic and higher-order model-checking. http://arxiv.org/abs/1501.04789. (accepted at CSL 2015)
  6. 6.
    Haddad, A.: Shape-preserving transformations of higher-order recursion schemes. Ph.D. thesis, Université Paris Diderot (2013)Google Scholar
  7. 7.
    Knapik, T., Niwiński, D., Urzyczyn, P.: Higher-order pushdown trees are easy. In: Nielsen, M., Engberg, U. (eds.) FOSSACS 2002. LNCS, vol. 2303, pp. 205–222. Springer, Heidelberg (2002) CrossRefGoogle Scholar
  8. 8.
    Melliès, P.A.: Categorical semantics of linear logic. In: Interactive Models of Computation and Program Behaviour, Panoramas et Synthses 27. pp. 1–196. Soci Mathmatique de France (2009)Google Scholar
  9. 9.
    Ong, C.H.L.: On model-checking trees generated by higher-order recursion schemes. In: LICS, pp. 81–90 (2006)Google Scholar
  10. 10.
    Salvati, S., Walukiewicz, I.: A model for behavioural properties of higher-order programs (2015). https://hal.archives-ouvertes.fr/hal-01145494
  11. 11.
    Terui, K.: Semantic evaluation, intersection types and complexity of simply typed lambda calculus. In: Tiwari, A. (ed.) RTA 2012. LIPIcs, vol. 15, pp. 323–338. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, Wadern (2012)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Laboratoire PPSUniversité Paris DiderotSorbonne Paris CitéFrance

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