# A decidability result for the halting problem of cellular automata in the pentagrid

## TL;DR

This paper proves that the halting problem for certain deterministic cellular automata in the pentagrid is decidable when starting from finite configurations with at most two states, including a quiescent state.

## Contribution

It establishes a decidability result for the halting problem of cellular automata in the pentagrid under specific initial conditions and state constraints.

## Key findings

- Halting problem is decidable for automata with up to two states in the pentagrid.
- Decidability holds when starting from finite configurations.
- One of the states must be quiescent.

## Abstract

In this paper, we investigate the halting problem for deterministic cellula automata in the pentagrid. We prove that the problem is decidable when the cellular automaton starts its computation from a finite configuration and when it has at most two states, one of them being a quiescent state.