O. Kullmann. A systematical approach to 3SAT -decision, yielding 3-SAT-decision in less than 1:5045 steps. Manuscript available from kullmann@mi.informatik.uni-frankfurt.de, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....arise. If we use a table to avoid recomputation, the recursion will run in polynomial time. 13 7.1. 3 SAT Applying our methods to the algorithm of Monien and Speckenmeyer [22] yields a simple MOL(1:62 ) algorithm for 3 SAT. Monien and Speckenmeyer s result has been improved several times [32, 19, 33]. Each of those papers gives a dsr, so our methods are applicable to all of them. Schiermeyer [33] claims a 1:497 time algorithm for 3 SAT. His algorithm is a dsr for 3 SAT. We will prove that 3SAT 2 REC(T (F ) where the function T (F ) 1:497 and will be defined below. We follow [33] to ....

O. Kullmann. A systematical approach to 3SAT -decision, yielding 3-SAT-decision in less than 1:5045 steps. Manuscript available from kullmann@mi.informatik.uni-frankfurt.de, 1995.

....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 ....

....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 gives the following very simple ....

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O. Kullmann. A systematical approach to 3-SAT-decision, yielding 3-SAT-decision in less than 1:4045 n steps. Manuscript available from kullmann@mi.informatik.uni-frankfurt.de, 1995.

....will arise. If we use a table to avoid recomputation, the recursion will run in polynomial time. 7.1. 3 SAT Applying our methods to the algorithm of Monien and Speckenmeyer [22] yields a simple MOL(1:62 n ) algorithm for 3 SAT. Monien and Speckenmeyer s result has been improved several times [32, 19, 33]. Each of those papers gives a dsr, so our methods are applicable to all of them. Schiermeyer [33] claims a 1:497 n time algorithm for 3 SAT. His algorithm is a dsr for 3 SAT. We will prove that 3SAT 2 REC(T (F ) where the function T (F ) 1:497 n and will be defined below. We follow [33] ....

O. Kullmann. A systematical approach to 3SAT -decision, yielding 3-SAT-decision in less than 1:5045 n steps. Manuscript available from kullmann@mi.informatik.uni-frankfurt.de, 1995.

....are in most cases manageable by electronic computers. Efforts have been made to reduce the amount of volume for DNA computers to solve NP complete problems [BCGT96,Ogi96,BF96] In this paper, we focus our attention to 3SAT. The current fastest sequential algorithm for 3SAT runs in 1:5 n steps [Kul96] If the algorithm is implemented on a computer that executes a million instructions in a second, the formulas of 60 variables will require approximately 10 hours; so there is no need to use DNA computers. If we double the size and set n = 120, then not only the sequential algorithm but also the ....

O. Kullmann. A systematical approach to 3-SAT-decision, yielding 3-SAT-decision in less than 1:5045 n steps. Manuscript, February 1996.

.... to the second approach, practical algorithms for 3SAT is a popular research topic and there have been introduced a number of deterministic, recursive search procedures: Davis and Putnam [DP60] Davis, Logemann, and Loveland [DLL62] Monien and Speckenmeyer [MS85] Schiermeyer [Sch93] and Kullmann [Kul96]. The first two, whose worst case analysis is yet to be done, have been widely used and studied [SK96, SML96, Fre96, CA96, GPB82, FP83, BPJ89, JB85] while the other three are proven to have time complexity respectively 1:618 n , 1:579 n , and 1:504 n . Among the five, the Davis Putnam ....

O. Kullmann. A systematical approach to 3-SAT-decision, yielding 3-SAT-decision in less than 1:5045 n steps. Manuscript, February 1996.

....are in this category. For still other classes of algorithms, it is known that they cannot be polynomially simulated by resolution proofs, and their precise complexity remains open. Extended Resolution [Tse68] is in this category. Recently, Kullmann introduced the concept of blocked clauses [Kul97b], with the property that they can be added to a formula or removed from a formula without affecting its satisfiability. Purdom s proposal for Complement Search [Pur84] as well as Tseitin s proposal for Extended Resolution [Tse68] can be cast as the introduction of blocked clauses [Kul97a] ....

....become empty. Thus EB = A B [ x; y] Gamma . Now modify the procedure of Section 5.1 (for the case of a leaf in the search) to return SB = EB in this case. 6 Conclusion All known proposed satisfiability algorithms that introduce blocked clauses use short clauses, having 2 3 literals [Pur84, Kul97b, Kul97a]. Introduction of new variables is excluded in these proposals. We have shown that such introductions can be polynomially simulated by resolution. The class of algorithms covered is quite broad, including those using any combination of resolution, elimination of an atom [DP60] and the splitting ....

O. Kullmann. A systematical approach to 3-SAT decision, yielding 3-SAT decision in less than 1:5045 n steps. Theoretical Computer Science, 1997. (to appear).

....in this section. The result SEPARATING SIGNS IN SAT 9 is eliminating from the formula pure literals (literals whose negations do not occur in the formula) 1 clauses, etc. In particular, at step (R4) we eliminate blocked clauses. The notion of a blocked clause was introduced by O. Kullmann in [8]. A blocked clause is a clause D containing a literal whose negation does not occur in clauses not containing the negation of another literal of D. In our case, we eliminate blocked clauses of a special form, namely, we eliminate each clause D such that in the formula F there is a clause C and ....

O. Kullmann, A systematical approach to 3-SAT-decision, yielding 3-SAT-decision in less than 1:5045 n steps, Theoretical Computer Science, to appear.

....00, 19xx Worst case Analysis, 3 SAT Decision and Lower Bounds: Approaches for Improved SAT Algorithms Oliver Kullmann Abstract. New methods for worst case analysis and (3 )SAT decision are presented. The focus lies on the central ideas leading to the improved bound 1:5045 n for 3 SAT 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 SAT algorithms is given and the only possibilities to remain under this bound are pointed out. In ....

....by a number of hypothesis . In addition an exponential lower bound for a general class of SAT algorithms is given and the only possibilities to remain under this bound are pointed out. In this article the central ideas leading to the improved worst case upper bound 1:5045 n for 3 SAT 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. ....

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Kullmann, O.: A systematical approach to 3-SAT-decision, yielding 3-SAT-decision in less than 1:5045 n steps. Submitted to: Theoretical Computer Science.

....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 ....

....Rule 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 ( ....

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Kullmann, O.: A systematical approach to 3-SAT-decision, yielding 3-SAT-decision in less than 1:5045 n steps.

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