On the readability of monotone boolean formulae

Khaled Elbassioni, Kazuhisa Makino, Imran Rauf

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

Golumbic et al. [Discrete Applied Mathematics 154(2006) 1465-1477] defined the readability of a monotone Boolean function f to be the minimum integer k such that there exists an ∧-∨-formula equivalent to f in which each variable appears at most k times. They asked whether there exists a polynomial-time algorithm, which given a monotone Boolean function f, in CNF or DNF form, checks whether f is a read-k function, for a fixed k. In this paper, we partially answer this question already for k=2 by showing that it is NP-hard to decide if a given monotone formula represents a read-twice function. It follows also from our reduction that it is NP-hard to approximate the readability of a given monotone Boolean function f:{0,1}n→{0,1} within a factor of . We also give tight sublinear upper bounds on the readability of a monotone Boolean function given in CNF (or DNF) form, parameterized by the number of terms in the CNF and the maximum size in each term, or more generally the maximum number of variables in the intersection of any constant number of terms. When the variables of the DNF can be ordered so that each term consists of a set of consecutive variables, we give much tighter polylogarithmic bounds on the readability.

Original languageBritish English
Title of host publicationComputing and Combinatorics - 15th Annual International Conference, COCOON 2009, Proceedings
Pages496-505
Number of pages10
DOIs
StatePublished - 2009
Event15th Annual International Conference on Computing and Combinatorics, COCOON 2009 - Niagara Falls, NY, United States
Duration: 13 Jul 200915 Jul 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5609 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference15th Annual International Conference on Computing and Combinatorics, COCOON 2009
Country/TerritoryUnited States
CityNiagara Falls, NY
Period13/07/0915/07/09

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