Infinite Time Cellular Automata: A Real Computation Model

TL;DR

This paper introduces infinite time cellular automata, a transfinite computation model equivalent in power to infinite time Turing machines, capable of simulating BSS machines in  steps.

Contribution

It presents a novel transfinite automaton model and demonstrates its computational equivalence to established models like infinite time Turing machines and BSS machines.

Findings

Infinite time cellular automata are as powerful as infinite time Turing machines.

They can simulate BSS machines in exactly  steps.

The model inherits properties from classical infinite time computation models.

Abstract

We define a new transfinite time model of computation, infinite time cellular automata. The model is shown to be as powerful than infinite time Turing machines, both on finite and infinite inputs; thus inheriting many of its properties. We then show how to simulate the canonical real computation model, BSS machines, with infinite time cellular automata in exactly \omega steps.