into propositional formulas, and by codifying matching into a propositional unsatisfiability problem. We distinguish between problems with conjunctive formulas and problems with disjunctive formulas, and present various optimizations. For instance, we propose a linear time algorithm which solves the first class

) are in an obvious sense 'elimination ' rules. In general, an elimination rule for a logical con-stant * allows an inference from a formula that has • as principal operator, i.e. an instance of such a rule has a (major) premiss P which has * as principal operator. In an application of such a rule

k-DL properly includes other well-known techniques for representing Boolean functions such as k-CNF (formulae in conjunctive normal form with at most k literals per clause), k-DNF (formulae in disjunctive normal form with at most k literals per term), and decision trees of depth k, our result

The programming language Scheme contains the control construct call/cc that allows access to the current continuation (the current control context). This, in effect, provides Scheme with first-class labels and jumps. We show that the well-known formulae-astypes correspondence, which relates a

We extend Clark's de nition of a completed program and the de nition of a loop formula due to Lin and Zhao to disjunctive logic programs. Our main result, generalizing the Lin/Zhao theorem, shows that answer sets for a disjunctive program can be characterized as the models of its

The propositional µ-calculus as introduced by Kozen in [4] is considered. The notion of disjunctive formula is defined and it is shown that every formula is semantically equivalent to a disjunctive formula. For these

Abstract. We consider the semantics equivalence between formulas and formulas in disjunctive normal form. In the settings of the standard µ-calculus, formulas and disjunctive formulas are equivalent. This question is open for timed extensions of the µ-calculus. Sorea has introduced a timed µ

, in turn, enables constructions in which predicates correspond to the evaluation of disjunctions, polynomials, CNF/DNF formulae, or threshold predicates (among others). Besides serving as a significant step forward in the theory of predicate encryption, our results lead to a number of applications

whether a propositional formula is satised by all models according to a given semantics. We concentrate on nite propositional disjunctive programs with as wells as without integrity constraints, i.e., clauses with empty heads; the problems are located in appropriate slots of the polynomial hierarchy

Contents 1 Introduction 3 2 Preliminaries 6 3 Computing a Minimum DNF 8 4 NP is Enough 11 5 Minimum Term DNF 13 5.2 The hA; Bi-version . . . . . . . . . . . . . . . . . . . . . . . . 17 5.3 Masek's Result . . . . . . . . . . . . . . . . . . . . . . . . . . 18 6 Minimum Length DNF 32 6.1 Length vs. Terms . . . . . . . . . . . . . . . . . . . . . . . . . 33 6.2 The A-version . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 6.3 The hA; Bi-version . . . . . . . . . . . . . . . . . . . . . . . . 35 6.4 The full truth-table version . . . . . . . . . . . . . . . . . . . 36 7 Minimum depth DNF 38 7.1 f is a Total Function . . . . . . . . . . . . . . . . . . . . . . . 40 7.2 f is a Partial Function . . . . . . . . . . . . . . . . . . . . . . 42 8 Approximation Hardness 42 8.1 Preserved Solution Values . . . . . . . . . . . . . . . . . . . . 43 8.2 Masek's Reduction . . . . . . . . . . . . . . . . . . . . . . . . 44 8.3 Reductions from X3C . . . . . . . . . . . . . . . . . . . . . . . 4