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Journal of Combinatorial Optimization

, Volume 22, Issue 3, pp 325–338 | Cite as

An improved time-space lower bound for tautologies

  • Scott Diehl
  • Dieter van Melkebeek
  • Ryan Williams
Article

Abstract

We show that for all reals c and d such that c 2 d<4 there exists a positive real e such that tautologies of length n cannot be decided by both a nondeterministic algorithm that runs in time n c , and a nondeterministic algorithm that runs in time n d and space n e . In particular, for every \(d<\sqrt[3]{4}\) there exists a positive e such that tautologies cannot be decided by a nondeterministic algorithm that runs in time n d and space n e .

Computational complexity Time-space lower bounds Tautologies Satisfiability 

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References

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Scott Diehl
    • 1
  • Dieter van Melkebeek
    • 1
  • Ryan Williams
    • 1
  1. 1.Department of Computer SciencesUniversity of Wisconsin-MadisonMadisonUSA

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