On the Readability of Monotone Boolean Formulae

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 paratially 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 montone Boolean function f : {0, 1}n → {0, 1} within a factor of O(n). We also give tight subinear upper bounds on the readability of a montone Boolean function given in CNF (or DNF) form, paramterized by the number of terms in the CNF and the maximum size in each term, or more generally ...

• Type: Conference
• Year: 2009
• Where: COCOON
• Authors: Khaled M. Elbassioni, Kazuhisa Makino, Imran Rauf
• Keywords: Boolean Function, COCOON 2009, Combinatorics, Monotone Boolean Function, Montone Boolean Function