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.

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.