Characterising Complexity Classes by Inductive Definitions in Bounded Arithmetic

Naohi Eguchi

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arXiv · 1306.5559

Characterising Complexity Classes by Inductive Definitions in Bounded Arithmetic

Naohi Eguchi

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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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BibTeX RIS

Naohi Eguchi. 2013-06-24. Characterising Complexity Classes by Inductive Definitions in Bounded Arithmetic. https://arxiv.org/abs/1306.5559

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