Abstract
If 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 result extends to every \(\Pi_t^p\)-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 such a hard sequence. Assuming that a problem Q has an almost optimal algorithm, we analyze whether every algorithm deciding Q, which is not almost optimal algorithm, has a hard sequence.
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Chen, Y., Flum, J., Müller, M. (2012). Hard Instances of Algorithms and Proof Systems. In: Cooper, S.B., Dawar, A., Löwe, B. (eds) How the World Computes. CiE 2012. Lecture Notes in Computer Science, vol 7318. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30870-3_13
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DOI: https://doi.org/10.1007/978-3-642-30870-3_13
Publisher Name: Springer, Berlin, Heidelberg
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