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Characterizing co-NL by a group action

Published online by Cambridge University Press:  05 December 2014

CLÉMENT AUBERT  and
THOMAS SEILLER
CLÉMENT AUBERT
Affiliation:
Université Paris 13, Sorbonne Paris Cité, LIPN, CNRS, (UMR 7030), F-93430, Villetaneuse, France Email: aubert@lipn.fr
THOMAS SEILLER
Affiliation:
I.H.É.S., Le Bois-Marie, 35, Route de Chartres, 91440 Bures-sur-Yvette, France Email: seiller@ihes.fr
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Abstract

In a recent paper, Girard (2012) proposed to use his recent construction of a geometry of interaction in the hyperfinite factor (Girard 2011) in an innovative way to characterize complexity classes. We begin by giving a detailed explanation of both the choices and the motivations of Girard's definitions. We then provide a complete proof that the complexity class co-NL can be characterized using this new approach. We introduce the non-deterministic pointer machine as a technical tool, a concrete model to compute algorithms.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 26 , Issue 4 , May 2016 , pp. 606 - 638
Copyright
Copyright © Cambridge University Press 2014 

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