where (~xn) ∈ B and B is a Boolean algebra. Only finite Boolean algebras are considered. The Boolean logic presented is based on the abstract Boolean algebra given by Huntington’s [14] postulates and on a special canonical form for a Boolean function given by Archie Blake [2]. The theory of reasoning is divided into functional and general parts, both of which seek antecedents or consequents of ...

In this paper, a new approach for enumerating the set prime implicants (PI) of a Boolean formula in conjunctive normal form (CNF) is proposed. It is based on an encoding of the input formula as a new one whose models correspond to the set of prime implicants of the original theory. This first PI enumeration approach is then enhanced by an original use of the boolean functions or gates usually i...

f(x1, . . . , xn) → {0, 1}, xi ∈ {0, 1}, i = 1, . . . , n assigns a value of 1 (TRUE) or 0 (FALSE ) to each of the 2 n-tuples that make up its domain. A Boolean function can be represented by a formula built using AND, OR and NOT operations. In this paper, ‘∗’ represents AND, ‘+’ represents OR, and x represents the negation NOT x (also called the complement of x). An AND of variables (some of w...

Constructing a small BDD from a given boolean formula depends on finding a good variable ordering. Finding a good order is NP-complete. In the past, methods based on heuristic analysis and formula (circuit) rewriting have shown to be useful for specific problem domains. We show that these methods need to be integrated: heuristic analysis can drive rewriting, which in turn simplifies analysis. W...

This paper introduces a new CNF encoding of pseudo-Boolean constraints, which allows unit propagation to maintain generalized arc consistency. In the worst case, the size of the produced formula can be exponentially related to the size of the input constraint, but some important classes of pseudo-Boolean constraints, including Boolean cardinality constraints, are encoded in polynomial time and ...

This paper describes and evaluates methods for implementing formula-speciic Boolean satissability (SAT) solver circuits in conngurable hardware. Starting from a general template design, our approach automatically generates VHDL for a circuit that is speciic to the particular Boolean formula being solved. Such an approach tightly customizes the circuit to a particular problem instance. Thus, it ...

In this paper the role of logic as a formal basis to exploit the query evaluation process of the boolean model and of weighted boolean models is analysed. The proposed approach is based on the expression of the constraint imposed by a query term on a document representation by means of the implication connective (by a fuzzy implication in the case of weighted terms). A logical formula correspon...

This paper presents PackUp (PACKage UPgradability with Boolean formulations) a framework for solving the the software package upgradability problem. Earlier versions of the framework (cudf2msu, cudf2pbo) participated in the 3rd MISC-live, an international competition organized by the European project MANCOOSI. The framework encodes the problem as a weighted partial MaxSAT formula and invokes a ...

In this report, we propose a quick survey of the currently known techniques for encoding a Boolean cardinality constraint into a cnf formula, and we discuss about the relevance of these encodings. We also propose models to facilitate analysis and design of cnf encodings for Boolean constraints.

We aim at investigating the solvability/insolvability of nondeterministic logarithmic-space (NL) decision, search, and optimization problems parameterized by natural size parameters using simultaneously polynomial time sub-linear space. are particularly focused on 2SAT3—a restricted variant 2CNF Boolean (propositional) formula satisfiability problem in which each variable a given appears most 3...