License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2015.14
URN: urn:nbn:de:0030-drops-54396
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2015/5439/
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Williams, R. Ryan

Thinking Algorithmically About Impossibility (Invited Talk)

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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.

BibTeX - Entry

@InProceedings{williams:LIPIcs:2015:5439,
  author =	{R. Ryan Williams},
  title =	{{Thinking Algorithmically About Impossibility (Invited Talk)}},
  booktitle =	{24th EACSL Annual Conference on Computer Science Logic (CSL 2015)},
  pages =	{14--23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-90-3},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{41},
  editor =	{Stephan Kreutzer},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5439},
  URN =		{urn:nbn:de:0030-drops-54396},
  doi =		{10.4230/LIPIcs.CSL.2015.14},
  annote =	{Keywords: satisfiability, derandomization, circuit complexity}
}

Keywords: satisfiability, derandomization, circuit complexity
Collection: 24th EACSL Annual Conference on Computer Science Logic (CSL 2015)
Issue Date: 2015
Date of publication: 07.09.2015

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