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NP trees and Carnap's modal logic

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1 Author(s)
Gottlob, G. ; Inst. fur Informationssysteme, Tech. Univ. Wien, Austria

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 Δ2P. 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. Using this result we show that the following problems are all PNP[O(logn)] 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, and checking whether a formula belongs to the stable set of beliefs generated by a propositional theory

Published in:

Foundations of Computer Science, 1993. Proceedings., 34th Annual Symposium on

Date of Conference:

3-5 Nov 1993