# On Modelling the Avoidability of Patterns as CSP

## TL;DR

This paper presents a unified CSP-based framework using MiniZinc to model and solve avoidability problems in string combinatorics, simplifying the process and leveraging standard solvers.

## Contribution

It introduces a novel, unified approach to model avoidability problems as CSPs in MiniZinc, replacing ad-hoc methods with a systematic framework.

## Key findings

- Successfully models various avoidability problems as CSPs
- Enables use of standard CSP solvers for these problems
- Simplifies the process of solving avoidability problems

## Abstract

Solving avoidability problems in the area of string combinatorics often requires, in an initial step, the construction, via a computer program, of a very long word that does not contain any word that matches a given pattern. It is well known that this is a computationally hard task. Despite being rather straightforward that, ultimately, all such tasks can be formalized as constraints satisfaction problems, no unified approach to solving them was proposed so far, and very diverse ad-hoc methods were used. We aim to fill this gap: we show how several relevant avoidability problems can be modelled, and consequently solved, in an uniform way as constraint satisfaction problems, using the framework of MiniZinc. The main advantage of this approach is that one is now required only to formulate the avoidability problem in the MiniZinc language, and then the actual search for a solution does not have to be implemented ad-hoc, being instead carried out by a standard CSP-solver.