Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

Structured Pigeonhole Principle, Search Problems and Hard Tautologies

Jan Krajíček
The Journal of Symbolic Logic
Vol. 70, No. 2 (Jun., 2005), pp. 619-630
Stable URL: http://www.jstor.org/stable/27588381
Page Count: 12
  • Read Online (Free)
  • Download ($10.00)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Structured Pigeonhole Principle, Search Problems and Hard Tautologies
Preview not available

Abstract

We consider exponentially large finite relational structures (with the universe {0.1}ⁿ) whose basic relations are computed by polynomial size (nO(1)) circuits. We study behaviour of such structures when pulled back by P/poly maps to a bigger or to a smaller universe. In particular, we prove that: 1. If there exists a P/poly map g: {0.1} → {0.1}m, n < m, iterable for a proof system then a tautology (independent of g) expressing that a particular size n set is dominating in a size 2ⁿ tournament is hard for the proof system. 2. The search problem WPHP, decoding RSA or finding a collision in a hashing function can be reduced to finding a size m homogeneous subgraph in a size 22m graph. Further we reduce the proof complexity of a concrete tautology (expressing a Ramsey property of a graph) in strong systems to the complexity of implicit proofs of implicit formulas in weak proof systems.

Page Thumbnails

  • Thumbnail: Page 
619
    619
  • Thumbnail: Page 
620
    620
  • Thumbnail: Page 
621
    621
  • Thumbnail: Page 
622
    622
  • Thumbnail: Page 
623
    623
  • Thumbnail: Page 
624
    624
  • Thumbnail: Page 
625
    625
  • Thumbnail: Page 
626
    626
  • Thumbnail: Page 
627
    627
  • Thumbnail: Page 
628
    628
  • Thumbnail: Page 
629
    629
  • Thumbnail: Page 
630
    630