Showing papers on "Disjunctive normal form published in 1968"
TL;DR: The maximal numberl(f) of conjunctions in a dead-end disjunctive normal form (d.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.f.
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→∞).
6 citations
TL;DR: Friedman showed that for certain classes of wffs, such as those in which m ≤ 2 or n = 0 in the prefix above, ⊢QM if and only if M* is the empty conjunct, the rules constitute a decision procedure.
Abstract: In [3], [4], and [5] Joyce Friedman formulated and investigated certain rules which constitute a semi-decision procedure for wffs of first order predicate calculus in closed prenex normal form with prefixes of the form ∀x1 ...∀xk∃y1 ...∃Ym∀z1 ...∀z n . Given such a wff QM,where Q is the prefix and M is the matrix in conjunctive normal form, Friedman’s rules can be used, in effect, to construct a matrix M* which is obtained from M by deleting certain conjuncts of M. Obviously, ⊢QM⊃QM* Using the Herbrand-Godel theorem for first order predicate calculus, Friedman showed that ⊢QM if and only if ⊢QM*. Clearly if M* is the empty conjunct (i.e., a tautology), ⊢QM* so ⊢QM. Friedman also showed that for certain classes of wffs, such as those in which m ≤ 2 or n = 0 in the prefix above, ⊢QM if and only if M* is the empty conjunct. Hence for such classes of wffs the rules constitute a decision procedure. Computer implementation [4] of the procedure has shown it to be quite efficient by present standards.
5 citations