Probabilistic Logic Gate in Asynchronous Game of Life with Critical Property

TL;DR

This paper explores how asynchronous cellular automata in the Game of Life can implement probabilistic logic gates at criticality, demonstrating phase transitions and optimal computability in perturbed environments.

Contribution

It introduces a novel approach to implementing probabilistic logic gates in asynchronous Game of Life automata at criticality, highlighting phase transition behavior and robustness.

Findings

Asynchronous GL exhibits a phase transition at criticality.

Density of state 1 decays with power law at critical point.

AND and OR gates perform well at criticality.

Abstract

Metaheuristic and self-organizing criticality (SOC) could contribute to robust computation under perturbed environments. Implementing a logic gate in a computing system in a critical state is one of the intriguing ways to study the role of metaheuristics and SOCs. Here, we study the behavior of cellular automaton, game of life (GL), in asynchronous updating and implement probabilistic logic gates by using asynchronous GL. We find that asynchronous GL shows a phase transition, that the density of the state of 1 decays with the power law at the critical point, and that systems at the critical point have the most computability in asynchronous GL. We implement AND and OR gates in asynchronous GL with criticality, which shows good performance. Since tuning perturbations play an essential role in operating logic gates, our study reveals the interference between manipulation and perturbation in probabilistic logic gates.