Characterising Complexity Classes by Inductive Definitions in Bounded Arithmetic
Logic
2014-01-21 v4
Abstract
Famous descriptive characterisations of P and PSPACE are restated in terms of the Cook-Nguyen style second order bounded arithmetic. We introduce an axiom of inductive definitions over second order bounded arithmetic. We show that P can be captured by the axiom of inflationary inductive definitions whereas PSPACE can be captured by the axiom of non-inflationary inductive definitions.
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Cite
@article{arxiv.1306.5559,
title = {Characterising Complexity Classes by Inductive Definitions in Bounded Arithmetic},
author = {Naohi Eguchi},
journal= {arXiv preprint arXiv:1306.5559},
year = {2014}
}
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Technical report