A Non-Deterministic Computation Model Based on Cellular Automata

Abstract

This paper proposes a novel computational model based on cellular automata (CA) that incorporates non-deterministic elements to better represent and simulate complex systems exhibiting inherently stochastic behavior. Traditional CA models operate under deterministic rules, limiting their applicability to systems with predictable outcomes. This work introduces a framework where each cell's state is influenced by its neighbors and a set of non-deterministic rules, mimicking the random interactions and probabilistic transitions prevalent in biological and physical systems. The model utilizes a grid-based structure, with each cell representing an entity within the system and its state determined by a combination of local interactions and random events. The core of the model lies in the definition of non-deterministic rules that govern state transitions, allowing for multiple possible outcomes for a given cell state and its neighborhood. This approach offers a flexible and powerful tool for modeling phenomena such as pattern formation, reaction-diffusion processes, and emergent behavior in biological systems, as well as complex physical dynamics. The model's design allows for the exploration of the impact of non-deterministic factors on system dynamics, providing a new perspective on modeling complex systems.