We study relationships between the class of Boolean formulas called exclusive-or expansions based on monotone DNF formulas (MDNF formulas, for short) and the class of Horn DNF formulas. An MDNF formula f is a Boolean formula represented by f = f1fd , where f1 > > fd are monotone DNF formulas and no terms appear more than once. A Horn DNF formula is a DNF formula where each term contains at most one negative literal. We show that the class of double Horn functions, where both f and its negation can be represented by Horn DNF formulas, coincides with a subclass of MDNF formulas such that each DNF formula fi consists of a single term. Furthermore, we give an incrementally polynomial time algorithm that transforms a given Horn DNF formula into the MDNF representation.

This paper concerns the issue of learning strategies for problem solvers from trace data. Many works on Explanation Based Learning have proposed methods for speeding up a given problem solver (or a Prolog program) by optimizing it on some subspace of problem instances with high probability of occurrences. However, in the current paper, we discuss the issue of identifying a target strategy exactly from trace data. Learning criterion used in this paper is the identification in the limit proposed by Gold. Further, we use the tree pattern language to represent preconditions of operators, and propose a class of strategies, called decision list strategies. One of the interesting features of our learning algorithm is the coupled use of state and operator sequence information of traces. Theoretically, we show that the proposed algorithm identifies some subclass of decision list strategies in the limit with the conjectures updated in polynomial time. Further, an experimental result on N-puzzle domain is presented.