Abstract
If the class TAUT of tautologies of propositional logic has no almost optimal algorithm, then every algorithm A deciding TAUT has a hard sequence, that is, a polynomial time computable sequence witnessing that A is not almost optimal. We show that this result extends to every Πt p-complete problem with t ≥1; however, assuming the Measure Hypothesis, there is a problem which has no almost optimal algorithm but is decided by an algorithm without hard sequences. For problems Q with an almost optimal algorithm, we analyze whether every algorithm deciding Q, which is not almost optimal, has a hard sequence.
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Index Terms
Hard Instances of Algorithms and Proof Systems
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CiE'12: Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computesIf the class Taut of tautologies of propositional logic has no almost optimal algorithm, then every algorithm $\mathbb{A}$ deciding Taut has a polynomial time computable sequence witnessing that $\mathbb{A}$ is not almost optimal. We show that this ...






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