# Logic Programming and Logarithmic Space

@article{Aubert2014LogicPA, title={Logic Programming and Logarithmic Space}, author={Cl{\'e}ment Aubert and Marc Bagnol and Paolo Pistone and Thomas Seiller}, journal={ArXiv}, year={2014}, volume={abs/1406.2110} }

We present an algebraic view on logic programming, related to proof theory and more specifically linear logic and geometry of interaction. Within this construction, a characterization of logspace (deterministic and non-deterministic) computation is given via a syntactic restriction, using an encoding of words that derives from proof theory.

## 11 Citations

### Unification and Logarithmic Space

- Computer Science, MathematicsRTA-TLCA
- 2014

An algebraic characterization of the complexity classes Logspace and NLogspace is presented, using an algebra with a composition law based on unification based on linear logic and Geometry of Interaction.

### Unary Resolution: Characterizing Ptime

- Computer ScienceFoSSaCS
- 2016

We give a characterization of deterministic polynomial time computation based on an algebraic structure called the resolution semiring, whose elements can be understood as logic programs or sets of…

### On the Resolution Semiring

- Computer Science, Mathematics
- 2014

This thesis studies a semiring structure with a product based on the resolution rule of logic programming that provides an algebraic and abstract setting, while being presented in a syntactic and concrete way, in which a theoretical study of computation can be carried on.

### Interaction Graphs: Nondeterministic Automata

- Computer ScienceArXiv
- 2016

This paper exhibits a series of semantic characterisations of sublinear nondeterministic complexity classes without reference to specific machine models that relate strongly to ICC results based on linear logic since the semantic framework considered stems from work on the latter.

### Interaction Graphs

- Computer ScienceACM Trans. Comput. Log.
- 2018

This article exhibits a series of semantic characterisations of sublinear nondeterministic complexity classes without reference to specific machine models, which relates strongly to icc results based on linear logic, since the semantic framework considered stems from work on the latter.

### PRAMs over integers do not compute maxflow efficiently

- Computer Science, MathematicsArXiv
- 2018

This article analyzes two proofs of complexity lower bound: Ben-Or's proof of minimal height of algebraic computational trees deciding certain problems and Mulmuley's proof that restricted Parallel Random Access Machines (prams) over integers can not decide P-complete problems efficiently.

### Memoization for Unary Logic Programming: Characterizing PTIME

- Computer ScienceArXiv
- 2015

A characterization of deterministic polynomial time computation based on an algebraic structure called the resolution semiring, whose elements can be understood as logic programs or sets of rewriting rules over first-order terms, and shows a PTIME-completeness result for a class of logic programming queries which use only unary function symbols.

### Towards a Complexity-through-Realizability Theory

- Computer ScienceArXiv
- 2015

The background, motivations and perspectives of this complexity-through-Realisability theory to be developed are provided, and it is illustrated with recent results.

### An in-between "implicit" and "explicit" complexity: Automata

- Computer Science, PsychologyArXiv
- 2015

This work surveys how automata theory contributed to complexity with a machine-dependant with implicit bounds model and makes two aspects implicit, by manipulating programming languages rather than models of com-putation and internalizing the bounds rather than using external measure.

### Entropy and Complexity Lower Bounds

- Computer Science, Mathematics
- 2018

The notion of topological entropy, which quantifies the exponential growth of the number of orbits of a dynamical system, is generalised to define the entropy of a graphing and is refined to more specific situations in which both the number and the degrees of the varieties delimiting the regions can be bounded.

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