Third-Order Idealized Algol with Iteration Is Decidable

  • Andrzej S. Murawski
  • Igor Walukiewicz
Conference paper

DOI: 10.1007/978-3-540-31982-5_13

Part of the Lecture Notes in Computer Science book series (LNCS, volume 3441)
Cite this paper as:
Murawski A.S., Walukiewicz I. (2005) Third-Order Idealized Algol with Iteration Is Decidable. In: Sassone V. (eds) Foundations of Software Science and Computational Structures. FoSSaCS 2005. Lecture Notes in Computer Science, vol 3441. Springer, Berlin, Heidelberg


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.

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

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