Almost every set in exponential time is P-bi-immune
Theoretical Computer Science
Bounded arithmetic, propositional logic, and complexity theory
Bounded arithmetic, propositional logic, and complexity theory
On an optimal propositional proof system and the structure of easy subsets of TAUT
Theoretical Computer Science - Complexity and logic
Complete Problems for Promise Classes by Optimal Proof Systems for Test Sets
COCO '98 Proceedings of the Thirteenth Annual IEEE Conference on Computational Complexity
On p-optimal proof systems and logics for PTIME
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Note: Speedup for natural problems and noncomputability
Theoretical Computer Science
LICS '11 Proceedings of the 2011 IEEE 26th Annual Symposium on Logic in Computer Science
Hardness hypotheses, derandomization, and circuit complexity
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
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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.