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On the frequency of the most frequently occurring variable in dual monotone DNFs

✍ Scribed by Vladimir Gurvich; Leonid Khachiyan

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 125 KB
Volume: 169
Category: Article
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(96)00090-8

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✦ Synopsis

Let f(x, ..... x.) ~-V/EF A,E1 Xi and ~(Xl ..... Xn) = VIEG A iEl Xi be a pair of dual monotone irredundant disjunctive normal forms, where F and G are the sets of the prime implicants of f and 9, respectively. For a variable xi, i = 1 ..... n, let #i = #{I E F[i E 1}/IFI and vi = #{I E Gli E I}/[G I be the frequencies with which xi occurs in f and 9. It is easily seen that max{#~, v~ ..... /~,, v,}/> 1/log(IF [ + IG[). We give examples of arbitrarily large F and G for which the above bound is tight up to a factor of 2.

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