## New methods for 3-SAT decision and worst-case analysis (1999)

Venue: | THEORETICAL COMPUTER SCIENCE |

Citations: | 65 - 12 self |

### BibTeX

@ARTICLE{Kullmann99newmethods,

author = {O. Kullmann},

title = {New methods for 3-SAT decision and worst-case analysis},

journal = {THEORETICAL COMPUTER SCIENCE},

year = {1999},

volume = {223},

pages = {1--72}

}

### Years of Citing Articles

### OpenURL

### Abstract

We prove the worst-case upper bound 1:5045 n for the time complexity of 3-SAT decision, where n is the number of variables in the input formula, introducing new methods for the analysis as well as new algorithmic techniques. We add new 2- and 3-clauses, called "blocked clauses", generalizing the extension rule of "Extended Resolution." Our methods for estimating the size of trees lead to a refined measure of formula complexity of 3-clause-sets and can be applied also to arbitrary trees. Keywords: 3-SAT, worst-case upper bounds, analysis of algorithms, Extended Resolution, blocked clauses, generalized autarkness. 1 Introduction In this paper we study the exponential part of time complexity for 3-SAT decision and prove the worst-case upper bound 1:5044:: n for n the number of variables in the input formula, using new algorithmic methods as well as new methods for the analysis. These methods also deepen the already existing approaches in a systematically manner. The following results...