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New methods for 3SAT decision and worstcase analysis
 THEORETICAL COMPUTER SCIENCE
, 1999
"... We prove the worstcase upper bound 1:5045 n for the time complexity of 3SAT 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 3clauses, called "blocked clauses", generalizing the e ..."
Abstract

Cited by 64 (12 self)
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We prove the worstcase upper bound 1:5045 n for the time complexity of 3SAT 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 3clauses, 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 3clausesets and can be applied also to arbitrary trees. Keywords: 3SAT, worstcase 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 3SAT decision and prove the worstcase 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...
An Improved Version of Width Restricted Resolution
, 1999
"... A new form of width restricted resolution, called "CUBI resolution" ("closure under bounded input resolution") is presented. CUBI resolution allows to eliminate the dependence on the maximal input clause length in the general lower bound for resolution from [BenSasson, Wigderson 99], and also t ..."
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A new form of width restricted resolution, called "CUBI resolution" ("closure under bounded input resolution") is presented. CUBI resolution allows to eliminate the dependence on the maximal input clause length in the general lower bound for resolution from [BenSasson, Wigderson 99], and also the polytime decidability problem about "kresolution" ([Kleine Buning 93]) is bypassed (by slightly strengthening the calculus). Generalizing the wellknown equivalence of the refutation power of Unit resolution and input resolution, CUBI resolution simulates "nested input resolution." 1 Introduction 1.1 Two forms of width restricted resolution Lower bounds for resolution complexity via width lower bounds 1975 Galil introduced bounded resolution in [9], using only clauses of bounded size, and he showed that certain Tseitintype formulas in 3CNF require very long clauses in any (full) resolution refutation, expressing hope, that this result might be useful for a superpolynomial lowe...