Mathematical systems theory

, Volume 13, Issue 1, pp 45–53 | Cite as

Satisfiability problems for propositional calculi

  • Harry R. Lewis


For each fixed set of Boolean connectives, how hard is it to determine satisfiability for formulas with only those connectives? We show that a condition sufficient for NP-completeness is that the functionx Λ ~ y be representable, and that any set of connectives not capable of representing this function has a polynomial-time satisfiability problem.


Computational Mathematic Propositional Calculus Satisfiability Problem Boolean Connective 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. A. Cook, The complexity of theorem-proving procedures,Proceedings of the Third ACM Symposium on the Theory of Computing, Shaker Heights, Ohio, pp. 151–158, 1971.Google Scholar
  2. 2.
    S. A. Cook and R. Reckhow, On the length of proofs in the propositional calculus,Proceedings of the Sixth ACM Symposium on the Theory of Computing, Seattle, Washington, pp. 135–148, 1974.Google Scholar
  3. 3.
    E. L. Post, The two-valued iterative systems of mathematical logic,Annals of Mathematics Studies,5, pp. 1–122, Princeton University Press, Princeton, New Jersey, 1941.Google Scholar
  4. 4.
    T. J. Schaefer, The complexity of satisfiability problems,Proceedings of the Tenth ACM Symposium on the Theory of Computing, San Diego, California, pp. 216–226, 1978.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1979

Authors and Affiliations

  • Harry R. Lewis
    • 1
  1. 1.Aiken Computation LaboratoryHarvard UniversityCambridgeUSA

Personalised recommendations