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Abstract: In this paper we analyze O''Hara''s partition bijection. We present three type of results. First, we show that O''Hara''s bijection can be viewed geometrically as a certain scissor congruence type result. Second, we obtain a number of new complexity bounds, proving that O''Hara''s bijection is efficient in several special cases and mildly exponential in general. Finally, we prove that for identities with finite support, the map of the O''Hara''s bijection can be computed in polynomial time, i.e. much more efficiently than by O''Hara''s construction. [Copyright &y& Elsevier]

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]