Third-Order Idealized Algol with Iteration Is Decidable

  • Andrzej S. Murawski
  • Igor Walukiewicz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3441)

Abstract

The problems of contextual equivalence and approximation are studied for the third-order fragment of Idealized Algol with iteration (IA\(^*_{3}\)). They are approached via a combination of game semantics and language theory. It is shown that for each (IA\(^{*}_{3}\))-term one can construct a pushdown automaton recognizing a representation of the strategy induced by the term. The automata have some additional properties ensuring that the associated equivalence and inclusion problems are solvable in Ptime. This gives an Exptime decision procedure for contextual equivalence and approximation for β-normal terms. Exptime-hardness is also shown in this case, even in the absence of iteration.

References

  1. 1.
    Reynolds, J.C.: The essence of Algol. In: Algorithmic Languages, pp. 345–372. North-Holland, Amsterdam (1981)Google Scholar
  2. 2.
    Abramsky, S., Ghica, D.R., Murawski, A.S., Ong, C.-H.L.: Applying game semantics to compositional software modelling and verification. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 421–435. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  3. 3.
    Alur, R., Madhusudan, P.: Visibly pushdown languages. In: Proc. of STOC, pp. 202–211 (2004)Google Scholar
  4. 4.
    Ghica, D.R., McCusker, G.: Reasoning about Idealized Algol using regular expressions. In: Welzl, E., Montanari, U., Rolim, J.D.P. (eds.) ICALP 2000. LNCS, vol. 1853, pp. 103–115. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  5. 5.
    Ong, C.-H.L.: Observational equivalence of 3rd-order Idealized Algol is decidable. In: Proc. of LICS, pp. 245–256 (2002)Google Scholar
  6. 6.
    Murawski, A.S.: On program equivalence in languages with ground-type references. In: Proc. of LICS, pp. 108–117 (2003)Google Scholar
  7. 7.
    Abramsky, S., McCusker, G.: Linearity, sharing and state: a fully abstract game semantics for Idealized Algol with active expressions. In: Algol-like languages, pp. 297–329. Birkhaüser, Basel (1997)Google Scholar
  8. 8.
    Hyland, J.M.E., Ong, C.-H.L.: On full abstraction for PCF. Information and Computation 163(2), 285–408 (2000)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Seidl, H.: Deciding equivalence of finite tree automata. SIAM J. Comput. 19(3), 424–437 (1990)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Andrzej S. Murawski
    • 1
  • Igor Walukiewicz
    • 2
  1. 1.Computing LaboratoryOxford UniversityOxfordUK
  2. 2.LaBRIUniversité Bordeaux-1TalenceFrance

Personalised recommendations