Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-25T19:32:45.899Z Has data issue: false hasContentIssue false
  • English
  • Français

Presburger arithmetic with unary predicates is Π11 complete

Published online by Cambridge University Press:  12 March 2014

Joseph Y. Halpern
Joseph Y. Halpern*
Affiliation:
IBM Almaden Research Center, San Jose, California 95120
Get access Rights & Permissions [Opens in a new window]

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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 56 , Issue 2 , June 1991 , pp. 637 - 642
Copyright
Copyright © Association for Symbolic Logic 1991

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[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. 148–153.Google Scholar
[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. 164–169.Google Scholar
[Ber80]Berman, L., The complexity of logical theories, Theoretical Computer Science, vol. 11 (1980), pp. 71–77.CrossRefGoogle Scholar
[End72]Enderton, H. B., A mathematical introduction to logic, Academic Press, New York, 1972.Google Scholar
[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. 27–42.Google Scholar
[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. 286–289.CrossRefGoogle Scholar
[HPS83]Harel, D., Pnueli, A., and Stavi, J., Propositional dynamic logic of nonregular programs, Journal of Computer and System Sciences, vol. 26 (1983), pp. 222–243.CrossRefGoogle Scholar
[Rog67]Rogers, H. Jr., Theory of recursive functions and effective computability, McGraw-Hill, New York, 1967.Google Scholar