Kullmann, O. and Luckhardt, H.: Various upper bounds on the complexity of algorithms for deciding propositional tautologies. Submitted to: Information and Computation.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....on worst case analysis of algorithms for NP hard problems. Several authors have described algorithms for maximum independent sets [4, 12, 13, 16] the best of these is Robson s [12] which takes time O(1:2108 n ) Several others have described algorithms for Boolean formula satisfiability [1, 7, 8, 9, 11, 14]; the best of these are Kullmann s [9] which solves 3 SAT in time O(1:5045 n ) 9] and Monien and Speckenmeyer s, which solves SAT in time O(1:2599 m ) For three coloring, we know of two relevant references. Lawler [6] is primarily concerned with the general chromatic number, but he also ....

O. Kullmann & H. Luckhardt. Various upper bounds on the complexity of algorithms for deciding propositional tautologies. Manuscript available from kullmann@mi.informatik.uni-frankfurt.de, 1994.

....formula, resolution, Davis Putnam procedure; DP schemes; blocked clauses, Extended resolution; generalized Autarkness; analysis of algorithms, size of trees, distance functions; k matching. Supported by DFG Leibniz Programm Schn 143 5 1. 1) For the history of the subject, see [Ku96] and also [KuLu96]; for the whole field of SAT algorithms see [GPFW96] c fl0000 American Mathematical Society 1 2 OLIVER KULLMANN of Maximal k matchings supplied with budgets ) In this way also the algorithmical disposition is clarified. 5. Two methods for generating new 2 clauses : The two main new methods ....

....maximal sums of edge valuations over all paths in T 1 resp. T 2 are comparable) See Lemma 2.1 in the next section. 1.3. Examples for distance functions d. 1. The differences of the basic measures: d(F; F 0 ) Deltam(F; F 0 ) m(F ) Gamma m(F 0 ) for m 2 f n; k; g. See Section 8 and [KuLu96] for worst case upper bounds with respect to these measures. 2. The basic measures can be combined by standardization: d(F; F 0 ) max Gamma Deltan=n; Deltak=k; Delta = Delta = max i n(F ) Gamma n(F 0 ) n(F ) k(F ) Gamma k(F 0 ) k(F ) F ) Gamma (F 0 ) F ) j ....

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Kullmann, O. and Luckhardt, H.: Various upper bounds on the complexity of algorithms for deciding propositional tautologies. Submitted to: Information and Computation.

....note on a generalization of Extended Resolution O. Kullmann Johann Wolfgang Goethe Universitat, Fachbereich Mathematik 60054 Frankfurt, Germany e mail: kullmann mi.informatik.uni frankfurt.de June 13, 1996 Abstract Motivated by improved SAT algorithms ( Ku96] [KuLu96]; yielding new worst case upper bounds) a natural parametrized 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 ....

....all three new clauses are blocked for the literal v respectively v (in any order of addition) and thus the addition of Blocked Clauses covers the Extension Rule. The concept of blocked clauses has been developped with the aim to improve worst case upper bounds for SAT algorithms. In [Ku96] and [KuLu96] the addition and elimination of blocked clauses under various circumstances is an important tool for improving the bound for 3 SAT decision (no clause has more than three literals) to 1:5045 n (n = number of variables) for improving the bound for SAT decision to 2 1=9 Delta ( number of ....

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Kullmann, O. and Luckhardt, H.: Various upper bounds on the complexity of algorithms for deciding propositional tautologies.

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