Skip to main content
×
Home
    • Aa
    • Aa

Characterizing co-NL by a group action

  • CLÉMENT AUBERT (a1) and THOMAS SEILLER (a2)
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.

Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

S. Arora and B. Barak (2009) Computational Complexity: A Modern Approach volume 1, Cambridge University Press.

C. Aubert (2011) Sublogarithmic uniform boolean proof nets. In: J. Y. Marion (ed.) Developements in Implicit Computational Complexity (DICE). Electronic Proceedings in Theoretical Computer Science 75 1527.

U. Dal Lago and M. Hofmann (2010) Bounded linear logic, revisited. Logical Methods in Computer Science 6 (4) 131.

V. Danos and J.-B. Joinet (2003) Linear logic & elementary time. Information and Computation 183 (1) 123137.

J. -Y. Girard (1989a) Geometry of interaction I: Interpretation of system f. Studies in Logic and the Foundations of Mathematics 127 221260.

J. -Y. Girard (2011) Geometry of interaction V: Logic in the hyperfinite factor. Theoretical Computer Science 412 (20) 18601883.

J. Y. Girard (2012) Normativity in logic In: P. Dybjer , S. Lindström , E. Palmgren and G. Sundholm (eds.) Epistemology versus Ontology. Logic, Epistemology, and the Unity of Science, volume 27, Springer 243263.

M. Hofmann , R. Ramyaa and U. Schöpp (2013) Pure pointer programs and tree isomorphism. In: F. Pfenning (ed.) FoSSaCS. Springer Lecture Notes in Computer Science 7794 321336.

Y. Lafont (2004) Soft linear logic and polynomial time. Theoretical Computer Science 318 (1) 163180.

G. J. Murphy (1990) C*-Algebras and Operator Theory, Academic Press Inc., Boston, MA.

A. Rosenberg (1966) On multi-head finite automata. IBM Journal of Research and Development 10 (5) 388394.

T. Seiller (2012b) Interaction graphs: Multiplicatives. Annals of Pure and Applied Logic 163 18081837.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 16 *
Loading metrics...

Abstract views

Total abstract views: 157 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 26th September 2017. This data will be updated every 24 hours.