Parameterized and subexponential-time complexity of satisfiability problems and applications

We study the parameterized and the subexponential-time complexity of the weighted and the unweighted satisfiability problems on bounded-depth normalized Boolean circuits. We establish relations between the subexponential-time complexity of the weighted and the unweighted satisfiability problems, and use them to derive relations among the subexponential-time complexity of several NP-hard problem. We then study the role of certain natural structural parameters of the circuit in characterizing the parameterized and the subexponential-time complexity of the circuit satisfiability problems under consideration. We obtain threshold functions on some circuit structural parameters, including the depth, the number of gates, the fan-in, and the maximum number of (variable) occurrences, that lead to tight characterizations of the parameterized and the subexponential-time complexity of the circuit satisfiability problems under consideration.

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