Thinking Algorithmically About Impossibility (Invited Talk)

Author R. Ryan Williams



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R. Ryan Williams

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R. Ryan Williams. Thinking Algorithmically About Impossibility (Invited Talk). In 24th EACSL Annual Conference on Computer Science Logic (CSL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 41, pp. 14-23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
https://doi.org/10.4230/LIPIcs.CSL.2015.14

Abstract

Complexity lower bounds like P != NP assert impossibility results for all possible programs of some restricted form. As there are presently enormous gaps in our lower bound knowledge, a central question on the minds of today's complexity theorists is how will we find better ways to reason about all efficient programs? I argue that some progress can be made by (very deliberately) thinking algorithmically about lower bounds. Slightly more precisely, to prove a lower bound against some class C of programs, we can start by treating C as a set of inputs to another (larger) process, which is intended to perform some basic analysis of programs in C. By carefully studying the algorithmic "meta-analysis" of programs in C, we can learn more about the limitations of the programs being analyzed. This essay is mostly self-contained; scant knowledge is assumed of the reader.
Keywords
  • satisfiability
  • derandomization
  • circuit complexity

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