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Polytime, combinatory logic and positive safe induction

Polytime, combinatory logic and positive safe induction  We characterize the polynomial time operations as those which are provably total in a first order system, which comprises (untyped) combinatory logic with extensionality, together with positive “safe induction” on the set of binary strings. The formalization of safe induction is inspired by Leivants idea of ramification. We also show how to replace ramification by means of modal logic. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Mathematical Logic Springer Journals

Polytime, combinatory logic and positive safe induction

Cantini, Andrea
Archive for Mathematical Logic , Volume 41 (2) – Feb 1, 2002
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Publisher
Springer Journals
Copyright
Copyright © 2002 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Mathematical Logic and Foundations; Mathematics, general; Algebra
ISSN
0933-5846
eISSN
1432-0665
DOI
10.1007/s001530100105
Publisher site
See Article on Publisher Site

Abstract

 We characterize the polynomial time operations as those which are provably total in a first order system, which comprises (untyped) combinatory logic with extensionality, together with positive “safe induction” on the set of binary strings. The formalization of safe induction is inspired by Leivants idea of ramification. We also show how to replace ramification by means of modal logic.

Journal

Archive for Mathematical Logic – Springer Journals

Published: Feb 1, 2002

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