Truemper, K.: Effective Logic Computation. Wiley (1998)  Home/Search   Document Not in Database   Summary   Related Articles   Check

....while modifying the system, this again means locating a minMUS, or at least a MUS or a low approximation unsatisfiable subformula. That is the part of the system that should not be changed. Clause Hardness Evaluation Many algorithms for the SAT problem have been proposed (see for instance [5,8,9,14] for extensive references) Most of complete methods are based on enumeration techniques and perform a tree search. They are also called Davis Putnam Loveland variants [7,12] and have the following general structure: DPL scheme (1) Choose a variable x according to a branching rule (see e.g. ....

K. Truemper. Effective Logic Computation. Wiley, New York, 1998

....reverse is true: testing satisfiability (resp. falsifiability) for DNF formulas can easily be reduced to testing falsifiability (resp. satisfiability) for CNF formulas. Other classes of formulas, such as Horn, extended Horn, q Horn, and SLUR, have been shown to be solved in polynomial time (see [9] for algorithms and credits) Recursively defined hierarchies of incrementally harder classes have also been defined and studied [3, 5, 7] Formulas on level k of these hierarchies typically can be solved in O(n k ) time. Downey and Fellows [4] considered hierarchies of problems. Levels of such ....

K. Truemper. Effective Logic Computation. To appear in 1996. 20

....polyhedron fx 2 R n : Ax e ; A)# 0 x eg has only integer extreme points. see [9, 31,15] for example) These polyhedra are the natural ones to study when formulating propositional logic problems in conjunctive normal form as linear 0,1 optimization problems (see [8, 38]) Let (A) 2 R m be defined by letting i (A) be the number of entries in row i of A that are equal to 1. Rewriting the defining system of the fractional generalized covering polyhedron as fx 2 R n : A)x ( A) e# 0 x eg # we see an immediate connection with our inequality ....

Klaus Truemper. Effective logic computation. Wiley,NewYork, 1998.

....covering polyhedron fx 2 R n : Ax e Gamma (A) 0 x eg has only integer extreme points. see [9, 31, 15] for example) These polyhedra are the natural ones to study when formulating propositional logic problems in conjunctive normal form as linear 0,1 optimization problems (see [8, 38]) Let (A) 2 R m be defined by letting i (A) be the number of entries in row i of A that are equal to 1. Rewriting the defining system of the fractional generalized covering polyhedron as fx 2 R n : GammaA)x ( GammaA) Gamma e; 0 x eg ; we see an immediate connection with our ....

Klaus Truemper. Effective logic computation. Wiley, New York, 1998.

....HALF SAT: Is there an assignment A which makes at least half of the nonisolated clauses in Sigma true as it is not MS 1 definable. More detailed applications of the methods presented in this paper for SAT and MAXSAT may be found in [59] They resemble the decomposition methods as discussed in [73] and based on [72] but the exact relationship to these decomposition methods still has to be investigated. 6 Feferman Vaught Shelah Theorem The proof of theorem 31 makes use of the Feferman Vaught Shelah Theorem for Monadic Second Order Logic and disjoint unions of relational structures. The ....

K. Truemper. Effective Logic Computation. John Wiley and Sons, 1998.

....take advantage of any efficient SAT solver and of any solver for the related minimization problem. For examples of SAT solvers, see GRASP (Marques Silva and Sakallah [4] SATO3 (Zhang [10] or relsat4 (Bayardo and Schrag [1] For an example of an effective solver for minimization, see Truemper [8]. Since a diagnosis system makes decisions based on the same theories, it is a suitable application for compilation and learning. We describe a solution algorithm for Q ALL SAT and its related problems and show how learning can be used. We also outline a compiler for a common case of Q ALL SAT ....

....W induces a subrange vector r of T for variable set W. Vector r has an entry rc for each clause c of T. If the assignment for W satisfies c, then rc = 1; otherwise, rc = 0 holds. A subrange vector r is feasible for T if there exists a T consistent truth assignment for W that induces r. Truemper [8] describes a class of CNF formulas that can be decomposed in few so called Boolean closed formulas. In such a case, the number of subrange vectors is restricted by a polynomial in the number of variables of U. A compiler can apply a learning scheme to U and can compute all subrange vectors of U ....

Truemper, K.: Effective Logic Computation. Wiley (1998)

....flexible and effective fully automated diagnostic system for hepatocellular carcinoma. 2. Preliminary Definitions In this section we provide a quick overview of the main concepts of propositional logic used in the rest of the paper. A complete presentation of such material can be found in [9]. A Boolean variable is a variable that may take on only the value True or False. One or more Boolean variables can be assembled in a Boolean formula using the not operator , the and operator , and the or operator . A Boolean formula where Boolean variables, possibly negated, are joined by ....

Truemper K. Effective Logic Computation. WileyInterscience, New York, 1998

....first decomposition assumes that, roughly speaking, the number of ways in which S feasible answers for the question variables can influence the values of the remaining variables is bounded. We call that decomposition exact linear since it is a special case of a logic decomposition called linear in Truemper [1998] and since it involves certain satisfiability subproblems where some clauses must not be satisfied. The second decomposition is in some sense the opposite of a logic decomposition called 2 monotone in the cited reference. For that reason, the decomposition considered here is called ....

....sense the opposite of a logic decomposition called 2 monotone in the cited reference. For that reason, the decomposition considered here is called antimonotone. The two decompositions described in this paper are compatible with, and thus may be combined with, logic decompositions described in Truemper [1998]. As a result, the large polynomially solvable classes of SAT and MINSAT established in that reference are readily modified to produce still large polynomially solvable classes of FUTILE SAT and FUTILE MINSAT. The paper proceeds as follows. Section 2 describes prior work. Section 3 introduces ....

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Truemper, K. (1998), Effective Logic Computation, Wiley, New York, 1998.

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Truemper, K. (1998), Effective Logic Computation (Wiley, New York, 1998).

....Method for Controlling Errors in Two Class Classification by G. Felici , F. S. Sun , and K. Truemper July, 1998 This research was supported in part by the Office of Naval Research under Grant N00014 93 1 0096. CNR IASI viale Manzoni 00185 Roma Italy University of Texas at Dallas Computer Science Program Box 830688 Richardson, Texas 75083 0688 U.S.A. Send all communications to: K. Truemper ....

....the logic minimization problems (6.6) and (6.7) We employ the Leibniz System (1996) for that task. That system analyzes each problem and compiles a solution algorithm. We execute that algorithm to obtain the desired solution. The mathematics underlying the Leibniz System (1996) is described in Truemper (1998). We should mention that the above logic based approach has uses beyond those summarized above. For example, the approach can account for classification costs in settings where getting information about any entry of a record entails a certain cost. As another example, the approach can produce ....

Truemper, K. (1998), Effective Logic Computation, Wiley, New York.

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