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Deciding propositional tautologies: Algorithms and their complexity
, 1997
"... We investigate polynomial reductions and efficient branching rules for algorithms deciding propositional tautologies for DNF and coNPcomplete subclasses. Upper bounds on the time complexity are given with exponential part 2 ff\Delta(F ) where (F ) is one of the measures n(F ) = #f variables g, ` ..."
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Cited by 38 (8 self)
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We investigate polynomial reductions and efficient branching rules for algorithms deciding propositional tautologies for DNF and coNPcomplete subclasses. Upper bounds on the time complexity are given with exponential part 2 ff\Delta(F ) where (F ) is one of the measures n(F ) = #f variables g, `(F ) = #f literal occurrences g and k(F ) = #f clauses g. We start with a discussion of variants of the algorithms from [Monien/Speckenmeyer85] and [Luckhardt84] with the known upper bound 2 0:695\Deltan for 3DNF and (roughly) (2 \Delta (1 \Gamma 2 \Gammap )) n for pDNF, p 3, where p is the maximal clause length, giving now an uniform treatment for all pDNF including the easy decidable case p 2. Recently for 3DNF the bound has been lowered to 2 0:5892\Deltan ([K2]; see also [Sch2], [K3]). In this article further improvements are achieved by studying two additional characteristic groups of parameters. The first group differentiates according to the maximal numbers (a; b) of occ...
Worstcase Analysis, 3SAT Decision and Lower Bounds: Approaches for Improved SAT Algorithms
"... . New methods for worstcase analysis and (3)SAT decision are presented. The focus lies on the central ideas leading to the improved bound 1:5045 n for 3SAT decision ([Ku96]; n is the number of variables). The implications for SAT decision in general are discussed and elucidated by a number of h ..."
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Cited by 22 (6 self)
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. New methods for worstcase analysis and (3)SAT decision are presented. The focus lies on the central ideas leading to the improved bound 1:5045 n for 3SAT decision ([Ku96]; n is the number of variables). The implications for SAT decision in general are discussed and elucidated by a number of hypothesis'. In addition an exponential lower bound for a general class of SATalgorithms is given and the only possibilities to remain under this bound are pointed out. In this article the central ideas leading to the improved worstcase upper bound 1:5045 n for 3SAT decision ([Ku96]) are presented. 1) In nine sections the following subjects are treated: 1. "Gauging of branchings": The " function" and the concept of a "distance function" is introduced, our main tools for the analysis of SAT algorithms, and, as we propose, also a basis for (complete) practical algorithms. 2. "Estimating the size of arbitrary trees": The " Lemma" is presented, yielding an upper bound for the number of l...
On a generalization of Extended Resolution
 Discrete Applied Mathematics
, 1997
"... Motivated by improved SAT algorithms ([13, 14, 15]; yielding new worst case upper bounds) a natural parameterized generalization GER of Extended Resolution (ER) is introduced. ER can simulate polynomially GER, but GER allows special cases for which exponential lower bounds can be proven. 1 Introduct ..."
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Cited by 17 (7 self)
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Motivated by improved SAT algorithms ([13, 14, 15]; yielding new worst case upper bounds) a natural parameterized generalization GER of Extended Resolution (ER) is introduced. ER can simulate polynomially GER, but GER allows special cases for which exponential lower bounds can be proven. 1 Introduction Extended Resolution G. Tseitin introduced in [21] the Extension Rule for the Resolution Calculus: F \Gamma! F [ n fv; a; bg; fv; ag; fv; bg o for arbitrary variables a; b and a new variable v (new relative to the set F of premises and to a; b). Thereby the clauseset \Phi fv; a; bg; fv; ag; fv; bg \Psi is the Conjunctive Normal Form of the formula v $ (a b). An Extended Resolution Proof (for short: ER proof) of the empty clause ? from the clauseset F is an ordinary resolution proof of ? from F , where F ' F is obtained by repeated applications of the Extension Rule. The length of an ER proof is the (total) number of (different) clauses in it. We denote by Comp ER (F...