# The Regularization of Small Sub-Constraint Satisfaction Problems

## TL;DR

This paper introduces a novel method for optimizing constraint satisfaction problems by replacing sub-CSPs with regular membership constraints, enhancing efficiency and propagation without increasing computational costs.

## Contribution

The paper presents a new approach to CSP optimization using local regular membership constraints, improving search efficiency and propagation while being applicable as a preprocessing step.

## Key findings

- Faster resolution speed compared to original CSPs
- Competitive performance with recent tabulation methods
- Applicable as a preprocessing step without conflicting with redundancy constraints

## Abstract

This paper describes a new approach on optimization of constraint satisfaction problems (CSPs) by means of substituting sub-CSPs with locally consistent regular membership constraints. The purpose of this approach is to reduce the number of fails in the resolution process, to improve the inferences made during search by the constraint solver by strengthening constraint propagation, and to maintain the level of propagation while reducing the cost of propagating the constraints. Our experimental results show improvements in terms of the resolution speed compared to the original CSPs and a competitiveness to the recent tabulation approach. Besides, our approach can be realized in a preprocessing step, and therefore wouldn't collide with redundancy constraints or parallel computing if implemented.