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Further results on propositional dynamic logic of nonregular programs

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Logics of Programs (Logic of Programs 1981)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 131))

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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 ∏ 11 -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 ∏ 11 -complete.

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References

  1. Fischer, M.J. and R.E. Ladner. Propositional dynamic logic of regular programs. J. Comp. Sys. Sciences, 18 (1979), pp. 194–211.

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  2. 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.

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  3. Pratt, V.R. Semantical considertions on Floyd-Hoare logic. Proc. 17th Symp. on Found. of Comp. Sc., (1976),pp. 109–121.

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  4. Pratt, V.R. A near optimal method for reasoning about action. J. Comp. Sys. Sciences, 20, (1980), pp. 231–254.

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  5. Rogers, H., Jr., Theory of Recursive Functions and Effective Computability. McGraw-Hill Co., New York, 1967.

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel

    D. Harel & A. Pnueli

  2. Department of Mathematics and Computer Science, Bar-Ilan University, Ramat-Gan, Israel

    D. Harel & J. Stavi

Authors
  1. D. Harel
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  2. A. Pnueli
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  3. J. Stavi
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Editor information

Dexter Kozen

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© 1982 Springer-Verlag Berlin Heidelberg

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Harel, D., Pnueli, A., Stavi, J. (1982). Further results on propositional dynamic logic of nonregular programs. In: Kozen, D. (eds) Logics of Programs. Logic of Programs 1981. Lecture Notes in Computer Science, vol 131. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0025779

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  • DOI: https://doi.org/10.1007/BFb0025779

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11212-9

  • Online ISBN: 978-3-540-39047-3

  • eBook Packages: Springer Book Archive

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