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Journal of Computer and System Sciences - Structure in Complexity Theory Conference, June 2-5, 1986
The Boolean hierarchy I: structural properties
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Functional oracle queries as a measure of parallel time
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A catalog of complexity classes
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Bounded queries to SAT and the Boolean hierarchy
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Generalizations of Opt P to the polynomial hierarchy
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Characterizations of Some Complexity Classes Between Theta^p_2 and Delta^p_2
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Collapsing Oracle Hierarchies, Census Functions and Logarithmically Many Queries
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Two remarks on the power of counting
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Nonmonotonic Reasoning is Sometimes Simpler
KGC '93 Proceedings of the Third Kurt Gödel Colloquium on Computational Logic and Proof Theory
Decision Procedure for Autoepistemic Logic
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Word problems requiring exponential time(Preliminary Report)
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Description logics of minimal knowledge and negation as failure
ACM Transactions on Computational Logic (TOCL)
Model Checking CTL+ and FCTL is Hard
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Redundancy in logic I: CNF propositional formulae
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A logical study of partial entailment
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In this paper we consider problems and complexity classes definable by interdependent queries to an oracle in NP. How the queries depend on each other is specified by a directed graph G. We first study the class of problems where G is a general dag and show that this class coincides with Dp2 .We then consider the class where G is a tree. Our main result states that this class is identical to PNP[O(log n)], the class of problems solvable in polynomial time with a logarithmic number of queries to an oracle in NP. This result has interesting applications in the fields of modal logic and artificial intelligence. In particular, we show that the following problems are all PNP[O(log n)] complete: validity-checking of formulas in Carnap's modal logic, checking whether a formula is almost surely valid over finite structures in modal logics K, T, and S4 (a problem recently considered by Halpern and Kapron [1992]), and checking whether a formula belongs to the stable set of beliefs generated by a propositional theory.We generalize the case of dags to the case where G is a general (possibly cyclic) directed graph of NP-oracle queries and show that this class corresponds to Pp2 . We show that such graphs are easily expressible in autoepistemic logic. Finally, we generalize our complexity results to higher classes of the polynomial-time hierarchy.