Variable and term removal from Boolean formulae

Abstract

Given a Boolean formula in disjunctive normal form, the variable deletion control set problem consists in finding a minimum cardinality set of variables whose deletion from the formula results in a DNF satisfying some prescribed property. Similar problems can be defined with respect to the fixation of variables or the deletion of terms in a DNF. In this paper, we investigate the complexity of such problems for a broad class of DNF properties.

Backdoor Sets of Quantified Boolean Formulas

“…The next result follows analogously to the corresponding result for propositional CNF formulas shown by Crama et al [8] and Nishimura et al [22].…”

Backdoor Sets of Quantified Boolean Formulas

“…These non-parameterized problems are NP-complete, justifying our parameterized approach. Membership follows immediately from Lemma 2 and hardness follows by trivial reduction from the non-quantified propositional versions, which have been shown by Crama et al [8] and Nishimura et al [22] to be NP-complete.…”

Linear Satisfiability Preserving Assignments

“…Symmetry breaking, which can be regarded as a generalization of satisfiability preserving assignments, is also widely used to reduce the search space in artificial intelligence (Freuder, 1991;Jeavons, Cohen, & Cooper, 1994;Prestwich, 2004). A backdoor set is a subset of variables whose instantiation leads a given formula to the one which is computationally easy to solve (Crama, Ekin, & Hammer, 1997;Williams, Gomes, & Selman, 2003;Gaspers & Szeider, 2012). …”