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An algorithm is proposed in this paper that finds exact exclusive-or sum-of-products of an arbitrary function, provided the number of product terms is less than eight. If the number of product terms in the minimal expression is more than seven, then the algorithm detects it and heuristically returns near-optimal expressions. The algorithm is time and space efficient even for functions with many input variables. [ABSTRACT FROM AUTHOR]

By combining the methods of two former papers of ours ([6] and [7]) we develop a finitary ordinal analysis of the axiom system KPi of Kripke-P atek set theory with an inaccessible universe. As a main result we obtain an upper bound (in the fast-growing hierarchy) for the provably recursive functions of KPi. [ABSTRACT FROM AUTHOR]

This paper discusses the problems of finding one of the largest similar substructures in tree Tb to tree Ta, where both Ta and Tb are rooted and ordered trees (RO-trees) or unrooted and cyclically ordered trees (CO-trees). A maximal closest common ancestor mapping and a largest similar substructure in Tb to Ta based on this mapping are defined and two algorithms are proposed for finding one of the largest similar substructures for RO-trees and that for CO-trees. The time and space complexities of the algorithm for RO-trees are OT(NaNb) and OS(NaNb), respectively; and those of the algorithm for CO-trees are OT(mambNaNb) and OS((ma + mb)NaNb), respectively, where ma(mb) and Na(Nb) are the largest degree of a vertex and the number of vertices of Ta(Tb), respectively. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(2): 92–104, 1997 [ABSTRACT FROM AUTHOR]