Quasi-acyclic propositional Horn knowledge bases: optimal compression

Horn knowledge bases are widely used in many applications. The paper is concerned with the optimal compression of propositional Horn production rule bases-one of the most important knowledge bases used in practice. The problem of knowledge compression is interpreted as a problem of Boolean function minimization. It was proved by P.L. Hammer and A. Kogan (1993) that the minimization of Horn functions, i.e., Boolean functions associated with Horn knowledge bases, is NP complete. The paper deals with the minimization of quasi acyclic Horn functions, the class of which properly includes the two practically significant classes of quadratic and of acyclic functions. A procedure is developed for recognizing in quadratic time the quasi acyclicity of a function given by a Horn CNF, and a graph based algorithm is proposed for the quadratic time minimization of quasi acyclic Horn functions