Data mining can be viewed, in many instances, as the task of computing a representation of a theory of a model or a database, in particular by finding a set of maximally specific sentences satisfying some property. We prove some hardness results that rule out simple approaches to solving the problem.The a priori algorithm is an algorithm that has been successfully applied to many instances of the problem. We analyze this algorithm, and prove that is optimal when the maximally specific sentences are "small". We also point out its limitations.We then present a new algorithm, the Dualize and Advance algorithm, and prove worst-case complexity bounds that are favorable in the general case. Our results use the concept of hypergraph transversals. Our analysis shows that the a priori algorithm can solve the problem of enumerating the transversals of a hypergraph, improving on previously known results in a special case. On the other hand, using results for the general case of the hypergraph transversal enumeration problem, we can show that the Dualize and Advance algorithm has worst-case running time that is sub-exponential to the output size (i.e., the number of maximally specific sentences).We further show that the problem of finding maximally specific sentences is closely related to the problem of exact learning with membership queries studied in computational learning theory.

Abstract: We introduce the notions of required precision and information content of datapath signals and use them to de ne functionally safe transformations on data ow graphs. These transformations reduce widths of datapath operators and enhance their mergeability. Using e cient algorithms to compute required precision and information content of signals, we de ne a new algorithm for partitioning a data ow graph consisting of datapath operators into mergeable clusters. Experimental results indicate that use of our clustering algorithm for operator merging based synthesis of datapath intensive designs, can lead to signi cant improvement in the delay and area of the implementation. 1.