Bounded Arithmetic and Descriptive Complexity

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 by showing that a language belongs to 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.

• Type: Conference
• Year: 2000
• Where: CSL
• Authors: Achim Blumensath
• Keywords: Automated Reasoning, CSL 2000, Free Monoid, Logical Characterisations, Transitive-closure Logics