Consistency of circuit evaluation , extended resolution and total NP search problems

@inproceedings{Krajek2016ConsistencyOC,
  title={Consistency of circuit evaluation , extended resolution and total NP search problems},
  author={Jan Kraj́ı{\vc}ek},
  year={2016}
}
  • Jan Kraj́ıček
  • Published 2016
We consider sets Γ(n, s, k) of narrow clauses expressing that no definition of a size s circuit with n inputs is refutable in resolution R in k steps. We show that every CNF with a short refutation in Extended R, ER, can be easily reduced to an instance of Γ(0, s, k) (with s, k depending on the size of the ER-refutation) and, in particular, that Γ(0, s, k) when interpreted as a relativized NP search problem is complete among all such problems provably total in bounded arithmetic theory V 1 1… CONTINUE READING

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