### Abstract

We present an algebraic characterization of the complexity classes Logspace and NLogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is rooted in proof theory and more specifically linear logic and geometry of interaction. We show how to build a model of computation in the unification algebra and then, by means of a syntactic representation of finite permutations in the algebra, we prove that whether an observation (the algebraic counterpart of a program) accepts a word can be decided within logarithmic space. Finally, we show that the construction naturally corresponds to pointer machines, a convenient way of understanding logarithmic space computation.

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

Article number | 6 |

Journal | Logical Methods in Computer Science |

Volume | 14 |

Issue number | 3 |

DOIs | |

State | Published - Jul 31 2018 |

### Fingerprint

### Keywords

- Geometry of interaction
- Geometry of interaction
- Implicit complexity
- Logarithmic space
- Pointer machines
- Proof theory
- Unification

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Logical Methods in Computer Science*,

*14*(3), [6]. https://doi.org/10.23638/LMCS-14(3:6)2018

**Unification and logarithmic space.** / Aubert, Clement; Bagnol, Marc.

Research output: Contribution to journal › Article

*Logical Methods in Computer Science*, vol. 14, no. 3, 6. https://doi.org/10.23638/LMCS-14(3:6)2018

}

TY - JOUR

T1 - Unification and logarithmic space

AU - Aubert, Clement

AU - Bagnol, Marc

PY - 2018/7/31

Y1 - 2018/7/31

N2 - We present an algebraic characterization of the complexity classes Logspace and NLogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is rooted in proof theory and more specifically linear logic and geometry of interaction. We show how to build a model of computation in the unification algebra and then, by means of a syntactic representation of finite permutations in the algebra, we prove that whether an observation (the algebraic counterpart of a program) accepts a word can be decided within logarithmic space. Finally, we show that the construction naturally corresponds to pointer machines, a convenient way of understanding logarithmic space computation.

AB - We present an algebraic characterization of the complexity classes Logspace and NLogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is rooted in proof theory and more specifically linear logic and geometry of interaction. We show how to build a model of computation in the unification algebra and then, by means of a syntactic representation of finite permutations in the algebra, we prove that whether an observation (the algebraic counterpart of a program) accepts a word can be decided within logarithmic space. Finally, we show that the construction naturally corresponds to pointer machines, a convenient way of understanding logarithmic space computation.

KW - Geometry of interaction

KW - Geometry of interaction

KW - Implicit complexity

KW - Logarithmic space

KW - Pointer machines

KW - Proof theory

KW - Unification

UR - http://www.scopus.com/inward/record.url?scp=85055825667&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85055825667&partnerID=8YFLogxK

U2 - 10.23638/LMCS-14(3:6)2018

DO - 10.23638/LMCS-14(3:6)2018

M3 - Article

VL - 14

JO - Logical Methods in Computer Science

JF - Logical Methods in Computer Science

SN - 1860-5974

IS - 3

M1 - 6

ER -