A Survey of Lower Bounds for Satisfiability and Related Problems

Dieter van Melkebeek
2006 Foundations and Trends® in Theoretical Computer Science  
Ever since the fundamental work of Cook from 1971, satisfiability has been recognized as a central problem in computational complexity. It is widely believed to be intractable, and yet till recently even a linear-time, logarithmic-space algorithm for satisfiability was not ruled out. In 1997 Fortnow, building on earlier work by Kannan, ruled out such an algorithm. Since then there has been a significant amount of progress giving non-trivial lower bounds on the computational complexity of
more » ... ability. In this article we survey the known lower bounds for the time and space complexity of satisfiability and closely related problems on deterministic, randomized, and quantum models with random access. We discuss the state-of-the-art results and present the underlying arguments in a unified framework.
doi:10.1561/0400000012 fatcat:vsdohimqr5a5zlbat3l37uwdem