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Mathematical systems theory

, Volume 15, Issue 1, pp 311–313 | Cite as

A note on complete sets and transitive closure

  • Ronald V. Book
  • Celia Wrathall
Article

Abstract

It is shown that there is a length-preserving relation that is NP-complete such that the transitive closure of the relation is PSPACE-complete.

Keywords

Computational Mathematic Transitive Closure 
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.

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References

  1. 1.
    R. Book. Polynomial space and transitive closure,SIAM J. Computing 8, 434–439 (1979)Google Scholar
  2. 2.
    S. Cook. The complexity of theorem-proving procedures,Proc. ACM Symp. Theory of Computing, 151–158 (1971).Google Scholar
  3. 3.
    J. Hartmanis and J. Simon. On the power of multiplication in random access machines,15th IEEE Symp. Switching and Automata Theory, 13–23 (1974).Google Scholar
  4. 4.
    N. Jones. Classes of automata and transitive closure,Info. Control 13, 207–229 (1968).Google Scholar
  5. 5.
    R. Karp. Reducibilities among combinatorial problems,Complexity of Computer Computations (R. Miller, J. Thatcher, eds.). New York: Plenum Press, 1972.Google Scholar
  6. 6.
    L. Stockmeyer. The polynomial-time hierarchy,Theoret. Comp. Sci. 3, 1–22 (1977).Google Scholar
  7. 7.
    C. Wrathall. Complete sets and the polynomial-time hierarchy,Theoret. Comp. Sci. 3, 23–33 (1977).Google Scholar

Copyright information

© Springer-Verlag New York Inc 1982

Authors and Affiliations

  • Ronald V. Book
    • 1
  • Celia Wrathall
    • 1
  1. 1.Department of MathematicsUniversity of California at Santa BarbaraSanta BarbaraUSA

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