Alternation-Trading Proofs, Linear Programming, and Lower Bounds

Abstract : A fertile area of recent research has demonstrated concrete polynomial time lower bounds for solving natural hard problems on restricted computational models. Among these problems are Satisfiability, Vertex Cover, Hamilton Path, Mod6-SAT, Majority-of-Majority-SAT, and Tautologies, to name a few. The proofs of these lower bounds follow a certain proof-by-contradiction strategy that we call alternation-trading. An important open problem is to determine how powerful such proofs can possibly be. We propose a methodology for studying these proofs that makes them amenable to both formal analysis and automated theorem proving. We prove that the search for better lower bounds can often be turned into a problem of solving a large series of linear programming instances. Implementing a small-scale theorem prover based on this result, we extract new human-readable time lower bounds for several problems. This framework can also be used to prove concrete limitations on the current techniques.
Complete list of metadatas

Cited literature [25 references]  Display  Hide  Download

https://hal.inria.fr/inria-00456011
Contributor : Publications Loria <>
Submitted on : Thursday, February 11, 2010 - 3:25:39 PM
Last modification on : Thursday, February 11, 2010 - 5:25:37 PM
Long-term archiving on : Friday, June 18, 2010 - 8:17:05 PM

File

williams.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : inria-00456011, version 1

Collections

Citation

Ryan Williams. Alternation-Trading Proofs, Linear Programming, and Lower Bounds. 27th International Symposium on Theoretical Aspects of Computer Science - STACS 2010, Inria Nancy Grand Est & Loria, Mar 2010, Nancy, France. pp.669-680. ⟨inria-00456011⟩

Share

Metrics

Record views

159

Files downloads

161