### 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.

Original language | English (US) |
---|---|

Pages (from-to) | 606-638 |

Number of pages | 33 |

Journal | Mathematical Structures in Computer Science |

Volume | 26 |

Issue number | 4 |

DOIs | |

State | Published - May 1 2016 |

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### ASJC Scopus subject areas

- Mathematics (miscellaneous)
- Computer Science Applications

### Cite this

*Mathematical Structures in Computer Science*,

*26*(4), 606-638. https://doi.org/10.1017/S0960129514000267

**Characterizing co-NL by a group action.** / Aubert, Clément; Seiller, Thomas.

Research output: Contribution to journal › Article

*Mathematical Structures in Computer Science*, vol. 26, no. 4, pp. 606-638. https://doi.org/10.1017/S0960129514000267

}

TY - JOUR

T1 - Characterizing co-NL by a group action

AU - Aubert, Clément

AU - Seiller, Thomas

PY - 2016/5/1

Y1 - 2016/5/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84916910092&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84916910092&partnerID=8YFLogxK

U2 - 10.1017/S0960129514000267

DO - 10.1017/S0960129514000267

M3 - Article

AN - SCOPUS:84916910092

VL - 26

SP - 606

EP - 638

JO - Mathematical Structures in Computer Science

JF - Mathematical Structures in Computer Science

SN - 0960-1295

IS - 4

ER -