A Polynomial Time Algorithm for Non-Disjoint Decomposition of Multiple-Valued Functions

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Venue:
ISMVL '04 Proceedings of the 34th International Symposium on Multiple-Valued Logic
Year:
2004

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Abstract

This paper addresses the problem of non-disjoint decompositionof multiple-valued functions. First, we show thatthe problem of computing non-disjoint decompositions of amultiple-valued function is related to the problem of findingmultiple-vertex dominators of a logic circuit, representingthe function. Second, we present an O(n^k) algorithm forcomputing all multiple-vertex dominators of a fixed size k,where n is the number of gates of the logic circuit. Our resultis important because no polynomial-time algorithm forfinding all possible non-disjoint decompositions of multiple-valuedfunctions is known. The presented approach allowsus computing a certain subset of non-disjoint decompositions(all reflected in a given circuit structure) in polynomialtime. A set of experiments on benchmark circuits illustratesthe efficiency of our approach.