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Logic of Programs 1981: Logics of Programs pp 124-136 | Cite as

Further results on propositional dynamic logic of nonregular programs

  • D. Harel
  • A. Pnueli
  • J. Stavi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 131)

Abstract

The main results of this paper are:
  1. (a)

    The validity problem for PDL with the single additional context-free program AΔ(B)AΔ, for atomic programs A,B, defined as \(\mathop \cup \limits_{i \geqslant o}\) Ai;B;Ai, is ∏ 1 1 -complete.

     
  2. (b)

    There exists a recursive (but nonregular) one-letter program L\(\subseteq\)A* such that the validity problem for PDL with the single additional program L is ∏ 1 1 -complete.

     

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References

  1. [FL]
    Fischer, M.J. and R.E. Ladner. Propositional dynamic logic of regular programs. J. Comp. Sys. Sciences, 18 (1979), pp. 194–211.CrossRefGoogle Scholar
  2. [HPS]
    Harel, D., A. Pnueli and J. Stavi. Propositional dynamic logic of context-free programs. 22nd IEEE Symp. on Found. of Comp. Sc., Nashville, Tenn., October 1981.Google Scholar
  3. [Pr1]
    Pratt, V.R. Semantical considertions on Floyd-Hoare logic. Proc. 17th Symp. on Found. of Comp. Sc., (1976),pp. 109–121.Google Scholar
  4. [Pr2]
    Pratt, V.R. A near optimal method for reasoning about action. J. Comp. Sys. Sciences, 20, (1980), pp. 231–254.CrossRefGoogle Scholar
  5. [R]
    Rogers, H., Jr., Theory of Recursive Functions and Effective Computability. McGraw-Hill Co., New York, 1967.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1982

Authors and Affiliations

  • D. Harel
    • 1
    • 2
  • A. Pnueli
    • 1
  • J. Stavi
    • 2
  1. 1.Department of Applied MathematicsWeizmann Institute of ScienceRehovotIsrael
  2. 2.Department of Mathematics and Computer ScienceBar-Ilan UniversityRamat-GanIsrael

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