# On optimal representatives of finite coloured linear orders

## TL;DR

This paper investigates finite coloured linear orders, providing algorithms to reduce structures to canonical forms under 2-equivalence, with detailed analysis for 2 and 3 move cases in Ehrenfeucht-Fraisse games.

## Contribution

It extends previous work by developing an algorithm for canonical reduction of finite coloured linear orders under 2-equivalence, focusing on 2 and 3 move scenarios.

## Key findings

- Algorithm for canonical form under 2-equivalence
- Analysis of 2 and 3 move Ehrenfeucht-Fraisse games
- Extended understanding of finite coloured linear orders

## Abstract

Two structures A and B are n-equivalent if player II has a winning strategy in the n-move Ehrenfeucht-Fraisse game on A and B. We extend earlier results about n-equivalence for finite coloured linear orders, describing an algorithm for reducing to canonical form under 2-equivalence, and concentrating on the cases of 2 and 3 moves.