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tascpl: TAS solver for Classical Propositional Logic
 In Logics in Artificial Intelligence, JELIA’04
, 2004
"... Abstract. We briefly overview the most recent improvements we have incorporated to the existent implementations of the TAS methodology, the simplified ∆tree representation of formulas in negation normal form. This new representation allows for a better description of the reduction strategies, in th ..."
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Abstract. We briefly overview the most recent improvements we have incorporated to the existent implementations of the TAS methodology, the simplified ∆tree representation of formulas in negation normal form. This new representation allows for a better description of the reduction strategies, in that considers only those occurrences of literals which are relevant for the satisfiability of the input formula. These reduction strategies are aimed at decreasing the number of required branchings and, therefore, control the size of the search space for the SAT problem. 1 Overview of TAS TAS denotes a family of refutational satisfiability testers for both classical and nonclassical logics which, like tableaux methods, also builds models for non valid formulas. So far, we have described algorithms for classical propositional logic [6,1], finitevalued propositional logics [3] and temporal logics [2]. The basis of the methodology is the alternative application of reduction strategies over formulas and a branching rule; the included reduction strategies are based on equivalence or equisatisfiability transformations whose complexity is at most quadratic; when no more simplifications can be applied, then the branching strategy is used and then the simplifications are called for. The power of the method is based not only on the intrinsically parallel design of the involved transformations, but also on the fact that these transformations are not just applied one after the other, but guided by some syntax directed criteria. 1.1 ∆Trees The improved version of the TAS satisfiability tester for classical propositional logic, tascpl, presented here uses and alternative representation of the boolean formulas: the simplified ∆tree representation [6]: in the same way that conjunctive normal forms are usually interpreted as lists of clauses, and disjunctive normal forms are interpreted as lists of cubes, we interpret negative normal forms as trees of clauses and cubes. In Fig. 1 an example is given in which a negation normal formula together with its ∆tree representation are shown: The part of the algorithm which obtains benefit from this more compact representation of negation normal formulas is the module of reduction strategies.
Satisfiability testing for Boolean formulas using Deltatrees
 Studia Logica
, 2002
"... The treebased data structure of #tree for propositional formulas is improved and optimised. The #trees allow a compact representation for negation normal forms as well as for a number of reduction strategies in order to consider only those occurrences of literals which are relevant for the satisf ..."
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The treebased data structure of #tree for propositional formulas is improved and optimised. The #trees allow a compact representation for negation normal forms as well as for a number of reduction strategies in order to consider only those occurrences of literals which are relevant for the satisfiability of the input formula. These reduction strategies are divided into two subsets (meaningand satisfiabilitypreserving transformations) and can be used to decrease the size of a negation normal form A at (at most) quadratic cost. The reduction strategies are aimed at decreasing the number of required branchings and, therefore, these strategies allow to limit the size of the search space for the SAT problem.
Verification in ACL2 of a generic framework to synthesize SATprovers
 In Logic Based Program Synthesis and Tranformation, LNCS 2664
, 2003
"... Abstract. We present in this paper an application of the ACL2 system to reason about propositional satisfiability provers. For that purpose, we present a framework where we define a generic transformation based SAT–prover, and we show how this generic framework can be formalized in the ACL2 logic, m ..."
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Abstract. We present in this paper an application of the ACL2 system to reason about propositional satisfiability provers. For that purpose, we present a framework where we define a generic transformation based SAT–prover, and we show how this generic framework can be formalized in the ACL2 logic, making a formal proof of its termination, soundness and completeness. This generic framework can be instantiated to obtain a number of verified and executable SAT–provers in ACL2, and this can be done in an automatized way. Three case studies are considered: semantic tableaux, sequent and Davis–Putnam methods. 1
A transformational decision procedure for nonclausal propositional formulas
 CoRR
"... A decision procedure for propositional logic is presented. This procedure is based on the DavisPutnam method. Propositional formulas are initially converted to negational normal form. This procedure determines whether a formula is valid or not by making validitypreserving transformations of fragme ..."
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A decision procedure for propositional logic is presented. This procedure is based on the DavisPutnam method. Propositional formulas are initially converted to negational normal form. This procedure determines whether a formula is valid or not by making validitypreserving transformations of fragments of the formula. At every iteration, a variable whose splitting leads to a minimal size of the transformed formula is selected. This procedure performs multiple optimizations. Some of them lead to removing fragments of the formula. Others detect variables for which a single truth value assignment is sufficient. Examples are presented.
Restricted trees and Reduction Theorems in MultipleValued Logics
"... In this paper we continue the theoretical study of the possible applications of the #tree data structure for multiplevalued logics, specifically, to be applied to signed propositional formulas. The #trees allow a compact representation for signed formulas as well as for a number of reduction s ..."
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In this paper we continue the theoretical study of the possible applications of the #tree data structure for multiplevalued logics, specifically, to be applied to signed propositional formulas. The #trees allow a compact representation for signed formulas as well as for a number of reduction strategies in order to consider only those occurrences of literals which are relevant for the satisfiability of the input formula. New and improved versions of reduction theorems for finitevalued propositional logics are introduced, and a satisfiability algorithm is provided which further generalise the TAS method [1, 5].