Note: Speedup for natural problems and noncomputability

  • Authors:
  • Hunter Monroe

  • Affiliations:
  • -

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2011

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Abstract

A resource-bounded version of the statement ''no algorithm recognizes all non-halting Turing machines'' is equivalent to an infinitely often (i.o.) superpolynomial speedup for the time required to accept any (paddable) coNP-complete language and also equivalent to a superpolynomial speedup in proof length in propositional proof systems for tautologies, each of which implies PNP. This suggests a correspondence between the properties ''has no algorithm at all'' and ''has no best algorithm'' which seems relevant to open problems in computational and proof complexity.