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...

We generalize [3, Lemma 2.2] and [4, Proposition 2.3] and deduce a positive result on Hilbert’s fourteenth problem. Further, we give a relatively transparent and elementary proof of [3, Theorem 1.1].

Given a Boolean formula in disjunctive normal form, the variable deletion control set problem consists in finding a minimum cardinality set of variables whose deletion from the formula results in a DNF satisfying some prescribed property. Similar problems can be defined with respect to the fixation of variables or the deletion of terms in a DNF. In this paper, we investigate the complexity of s...

We analyze an algorithm that in each free step Selects & Sets to a value a pair of complementary literals of specified corresponding degrees. Unit Clauses, if they exist, are given priority. This algorithm is proved to succeed on input random 3-CNF formulas of density c3 = 3.52+, establishing that the conjectured threshold value for random 3CNF formulas is at least 3.52+.

The concepts of MSS (Maximal Satisfiable Subset) and CoMSS (also called Minimal Correction Subset) play a key role in many A.I. approaches and techniques. In this paper, a novel algorithm for partitioning a Boolean CNF formula into one MSS and the corresponding CoMSS is introduced. Extensive empirical evaluation shows that it is more robust and more efficient on most instances than currently av...

In this paper we give a geometric realization of free solvable groups, and study its Poisson-Furstenberg boundaries, we also discuss the construction of normal forms in the solvable groups.