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Presburger arithmetic with unary predicates is Π11 complete

  • Joseph Y. Halpern (a1)

Abstract

We give a simple proof characterizing the complexity of Presburger arithmetic augmented with additional predicates. We show that Presburger arithmetic with additional predicates is complete. Adding one unary predicate is enough to get hardness, while adding more predicates (of any arity) does not make the complexity any worse.

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[AH89a]Abadi, M. and Halpern, J. Y., Decidability and expressiveness for first-order logics of probability, Proceedings of the 30th IEEE symposium on foundations of computer science, IEEE Computer Society Press, Washington, D.C., 1989, pp. 148153.
[AH89b]Alur, R. and Henzinger, T. A., A really temporal logic, Proceedings of the 30th IEEE symposium on foundations of computer science, IEEE Computer Society Press, Washington, D.C., 1989, pp. 164169.
[Ber80]Berman, L., The complexity of logical theories, Theoretical Computer Science, vol. 11 (1980), pp. 7177.
[End72]Enderton, H. B., A mathematical introduction to logic, Academic Press, New York, 1972.
[FR74]Fischer, M. J. and Rabin, M. O., Super-exponential complexity of Presburger arithmetic, Complexity of computation (Karp, R. M., editor), SIAM-AMS Proceedings, vol. 7, American Mathematical Society, Providence, Rhode Island, 1974, pp. 2742.
[GS74]Garfunkel, S. and Schmerl, J. H., The undecidability of theories of groupoids with an extra predicate, Proceedings of the American Mathematical Society, vol. 42 (1974), pp. 286289.
[HPS83]Harel, D., Pnueli, A., and Stavi, J., Propositional dynamic logic of nonregular programs, Journal of Computer and System Sciences, vol. 26 (1983), pp. 222243.
[Rog67]Rogers, H. Jr., Theory of recursive functions and effective computability, McGraw-Hill, New York, 1967.

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Presburger arithmetic with unary predicates is Π11 complete

  • Joseph Y. Halpern (a1)

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