Hardness Hypotheses, Derandomization, and Circuit Complexity

  • John M. Hitchcock
  • A. Pavan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3328)


We consider three complexity-theoretic hypotheses that have been studied in different contexts and shown to have many plausible consequences.

The Measure Hypothesis: NP does not have p-measure 0.

The pseudo-NP Hypothesis: there is an NP Language L such that any DTIME \(2^{{n^\epsilon}}\) Language L’ can be distinguished from L by an NP refuter.

The NP-Machine Hypothesis: there is an NP machine accepting 0* for which no \(2^{{n^\epsilon}}\)-time machine can find infinitely many accepting computations.

We show that the NP-machine hypothesis is implied by each of the first two. Previously, no relationships were known among these three hypotheses. Moreover, we unify previous work by showing that several derandomization and circuit-size lower bounds that are known to follow from the first two hypotheses also follow from the NP-machine hypothesis. We also consider UP versions of the above hypotheses as well as related immunity and scaled dimension hypotheses.


Boolean Function Circuit Complexity Measure Hypothesis Oracle Gate Oracle Circuit 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • John M. Hitchcock
    • 1
  • A. Pavan
    • 2
  1. 1.Department of Computer ScienceUniversity of Wyoming 
  2. 2.Department of Computer ScienceIowa State University 

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