Bell's theorem in automata theory

TL;DR

This paper reformulates Bell's theorem within automata theory, demonstrating that finite probabilistic machines cannot replicate quantum Bell test results when independent of remote inputs.

Contribution

It introduces a purely mathematical automata-theoretic proof of Bell's theorem, removing physical and ontological assumptions from the original formulation.

Findings

Finite probabilistic automata cannot reproduce quantum Bell test statistics under independence.

The reformulation provides a new mathematical perspective on quantum nonlocality.

The approach avoids physical notions, focusing solely on automata theory principles.

Abstract

Bell's theorem is reformulated and proved in the pure mathematical terms of automata theory, avoiding any physical or ontological notions. It is stated that no pair of finite probabilistic sequential machines can reproduce in its output the statistical results of the quantum-physical Bell test experiment if each machine is independent of the respective remote input.