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On Constructing Minimal Formulae

By Paul E. Dunne


Given a Boolean propositional formula, ϕ(Xn) over the basis Ω = {∧, ∨, ¬} we consider the following decision problem: is there a subset of literals, S, for which ϕ(Xn) ≡ ∧ y∈S y or ϕ(Xn) ≡ ∨ y∈S y? We prove that the “obvious ” Σp2 upper bound is sub-optimal and that the problem is decidable in P NP the class of languages decidable by polynomial time methods allowed to make non-adaptive queries to an NP oracle. We further show that the associated function problem of computing a witnessing such subset when one exists can be solved in FP N

Year: 2009
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