On the greatest length of a dead-end disjunctive normal form for almost all Boolean functions

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 1968 English Publisher:Springer Science and Business Media LLCJournal:Mathematical Notes of the Academy of Sciences of the USSR, volume 4, pages 881-886 (issn: 0001-4346, eissn: 1573-8876,

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Authors: Sapozhenko, A. A.;

doi: 10.1007/bf01110822

On the greatest length of a dead-end disjunctive normal form for almost all Boolean functions

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Abstract

The maximal numberl(f) of conjunctions in a dead-end disjunctive normal form (d.n.f.) of a Boolean functionf and the numberτ (f) of dead-end d.n.f. are important parameters characterizing the complexity of algorithms for finding minimal d.n.f. It is shown that for almost all Boolean functionsl(f)2n−1, log2τ(f)2n−1log2nlog2log2n (n→∞).

Related Organizations

Russian Academy of Sciences
Russian Federation

Keywords

languages, automata, networks

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