Abstract

We investigate polynomial reductions and efficient branching rules for algorithms deciding propositional tautologies for DNF and coNP--complete 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 3-DNF and (roughly) (2 \Delta (1 \Gamma 2 \Gammap )) n for p-DNF, p 3, where p is the maximal clause length, giving now an uniform treatment for all p-DNF including the easy decidable case p 2. Recently for 3-DNF 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...

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