# Reachability Problem in Non-uniform Cellular Automata

## TL;DR

This paper introduces an algorithm to determine configuration reachability in non-uniform cellular automata, utilizing a reachability tree, with good average performance despite exponential worst-case complexity.

## Contribution

It presents the first decision algorithm for the configuration reachability problem in non-uniform cellular automata using a novel reachability tree method.

## Key findings

- Algorithm effectively decides reachability in non-uniform CAs.
- Reachability tree provides a useful characterization tool.
- Average performance of the algorithm is very good despite exponential worst-case complexity.

## Abstract

This paper deals with the CREP (Configuration REachability Problem) for non-uniform cellular automata (CAs). The cells of non-uniform CAs, we have considered here, can use different Wolfram's rules to generate their next states. We report an algorithm which decides whether or not a configuration of a given (non-uniform) cellular automaton is reachable from another configuration. A characterization tool, named Reachability tree, is used to develop theories and the decision algorithm for the CREP. Though the worst case complexity of the algorithm is exponential in time and space, but the average performance is very good.