TR11-085 Authors: Yijia Chen, Joerg Flum, Moritz Müller

Publication: 30th May 2011 13:27

Downloads: 2772

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Assuming that the class TAUT of tautologies of propositional logic has no almost optimal algorithm, we show that every algorithm $\mathbb A$ deciding TAUT has a polynomial time computable sequence witnessing that $\mathbb A$ is not almost optimal. The result extends to every $\Pi_t^p$-complete problem with $t\ge 1$; however, we show that assuming the Measure Hypothesis there is a problem which has no almost optimal algorithm but has an algorithm without hard sequences.