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We consider the extension of Boolean circuits to quantified Boolean circuits by adding universal and existential quantifier nodes with semantics adopted from quantified Boolean formulas (QBF). The concept allows not only prenex representations of the form ∀x1∃y1...∀xn∃yn c where c is an ordinary Boolean circuit with inputs x1,. We also consider more general(More)
In this paper, quantified Horn formulas (QHORN) are investigated. We prove that the behavior of the existential quantifiers depends only on the cases where at most one of the universally quantified variables is zero. Accordingly, we give a detailed characterization of QHORN satisfiability models which describe the set of satisfying truth assignments to the(More)
In this paper, we consider the problem of compactly representing nested instantia-tions of propositional subformulas with different arguments as quantified Boolean formulas (QBF). We develop a generic QBF encoding pattern which combines and generalizes existing QBF encoding techniques for simpler types of redundancy. We obtain an equivalence-preserving(More)
In this paper, quantified Horn formulas with free variables (QHORN *) are investigated. The main result is that any quantified Horn formula Φ of length |Φ| with free variables, |∀| universal quantifiers and an arbitrary number of existential quantifiers can be transformed into an equivalent formula of length O(|∀| · |Φ|) which contains only existential(More)
We present an extension of Q-Unit resolution for formulas that are not completely in clausal form. This b-unit resolution is applied to different classes of quantified Boolean formulas in which the existen-tial and universal variables satisfy the Horn property. These formulas are transformed into propositional equivalents consisting of only polynomially(More)