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ON OPTIMAL INVERTERS

Published online by Cambridge University Press:  13 May 2014

YIJIA CHEN  and
JÖRG FLUM
YIJIA CHEN
Affiliation:
DEPARTMENT OF COMPUTER SCIENCE, SHANGHAI JIAOTONG UNIVERSITY, XUHUI, SHANGHAI, CHINAE-mail:[email protected]
JÖRG FLUM
Affiliation:
MATHEMATISCHES INSTITUT, ALBERT-LUDWIGS-UNIVERSITÄT FREIBURG, FREIBURG IM BREISGAU, BADEN-WÜRTTEMBERG, GERMANYE-mail:[email protected]
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Abstract

Leonid Levin showed that every algorithm computing a function has an optimal inverter. Recently, we applied his result in various contexts: existence of optimal acceptors, existence of hard sequences for algorithms and proof systems, proofs of Gödel’s incompleteness theorems, analysis of the complexity of the clique problem assuming the nonuniform Exponential Time Hypothesis. We present all these applications here. Even though a simple diagonalization yields Levin’s result, we believe that it is worthwhile to be aware of the explicit result. The purpose of this survey is to convince the reader of our view.

Type
Articles
Information
Bulletin of Symbolic Logic , Volume 20 , Issue 1 , March 2014 , pp. 1 - 23
Copyright
Copyright © The Association for Symbolic Logic 2014 

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