Thinking Algorithmically About Impossibility (Invited Talk)

Author R. Ryan Williams

Thumbnail PDF


  • Filesize: 449 kB
  • 10 pages

Document Identifiers

Author Details

R. Ryan Williams

Cite AsGet BibTex

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)


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.
  • satisfiability
  • derandomization
  • circuit complexity


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail