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/
Williams, R. Ryan
Thinking Algorithmically About Impossibility (Invited Talk)
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: |
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satisfiability, derandomization, circuit complexity |
Collection: |
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24th EACSL Annual Conference on Computer Science Logic (CSL 2015) |
Issue Date: |
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2015 |
Date of publication: |
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07.09.2015 |