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On the complexity of Boolean functions with small number of ones
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N. P. Redkin
Published/Copyright:
October 1, 2004
We consider the class of Boolean functions Fn,k consisting of all functions in n variables such that each of them takes value one exactly for k tuples of variables. We obtain linear in n estimates of the complexity of realisation of functions in Fn,k by circuits of functional elements over the basis containing all Boolean functions in two variables except the linear functions x ⊕ y and x ⊕ y ⊕ 1. It follows from these estimates that for small k, for example, for k < ln n, the well-known Finikov method provides asymptotically minimal circuits for all functions of Fn,k. In some cases, the known lower bounds for complexity of circuits give a possibility to prove the minimality of the corresponding circuits.
Published Online: 2004-10-01
Published in Print: 2004-10-01
Copyright 2004, Walter de Gruyter
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