# Logical Gates via Gliders Collisions

## TL;DR

This paper demonstrates how logical gates, including reversible ones like Fredkin and CNOT, can be implemented through collisions of gliders in a cellular automaton with memory, showcasing potential for computation.

## Contribution

It introduces novel designs of logical gates using glider collisions in a cellular automaton with memory, expanding computational possibilities.

## Key findings

- Successfully implemented Fredkin and CNOT gates via glider collisions.
- Demonstrated the use of cellular automaton with memory for logical operations.
- Showed that glider interactions can form the basis of reversible computation.

## Abstract

An elementary cellular automaton with memory is a chain of finite state machines (cells) updating their state simultaneously and by the same rule. Each cell updates its current state depending on current states of its immediate neighbours and a certain number of its own past states. Some cell-state transition rules support gliders, compact patterns of non-quiescent states translating along the chain. We present designs of logical gates, including reversible Fredkin gate and controlled NOT gate, implemented via collisions between gliders.