Bounded arithmetic, propositional logic, and complexity theory
Bounded arithmetic, propositional logic, and complexity theory
Foundations of Databases: The Logical Level
Foundations of Databases: The Logical Level
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We study definability of languages in arithmetic and the free monoid by bounded versions of fixed-point and transitive-closure logics. In particular we give logical characterisations of complexity classes C by showing that a language belongs to C if and only if it is definable in either arithmetic or the free monoid by a formula of a certain logic. We investigate in which cases the bounds of fixed-point operators may be omitted. Finally, a general translation of results from descriptive complexity to the approach described in this paper is presented.