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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 66 (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...
Algorithms for SAT/TAUT decision based on various measures
 Information and Computation
, 1999
"... We investigate algorithms deciding propositional tautologies for DNF and coNPcomplete subclasses given by restrictions on the number of occurrences of literals. Especially polynomial use of resolution for reductions in combination with a new combinatorial principle called "Generalized Sign Princip ..."
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Cited by 11 (8 self)
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We investigate algorithms deciding propositional tautologies for DNF and coNPcomplete subclasses given by restrictions on the number of occurrences of literals. Especially polynomial use of resolution for reductions in combination with a new combinatorial principle called "Generalized Sign Principle" is studied. Upper bounds on time complexity are given with exponential part 2 ff\Delta(F ) where the measure (F ) for a clause set F either is the number n(F ) of variables, the number `(F ) of literal occurrences or the number k(F ) of clauses. ff is called a "power coefficient" for the class of formulas under consideration w.r.t. measure . Power coefficients are derived with the help of a method estimating the size of trees, which is also used to find "good" branching rules. Under natural conditions power coefficients ff; fi; fl for n; k; ` respectively fulfill ff fi fl. We obtain the following power coefficients.  0:1112 for DNF w.r.t. `  0:3334 for DNF w.r.t. k These result...