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In this paper, we introduce the notion of models for quantified Boolean formulas. For various classes of quantified Boolean formulas and various classes of Boolean functions, we investigate the problem of determining whether a model exists. Furthermore, we show for these classes the complexity of the model checking problem, which is to check whether a given(More)
Using auxiliary variables to introduce definitions is a popular and powerful technique in knowledge representation which can lead to shorter and more natural encodings without long repetitions. In this paper, we formally define the notion of auxiliary variables and then examine their expressive power and discuss interesting applications. We relate the idea(More)
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, ..., xn, y1, ..., yn. We also(More)