A Simulation of Oblivious Multi-Head One-Way Finite Automata by Real-Time Cellular Automata

TL;DR

This paper demonstrates how oblivious multi-head one-way finite automata can be simulated by cellular automata in real time, highlighting the potential for real-time simulation of certain sequential models.

Contribution

It introduces a method to simulate oblivious multi-head one-way finite automata using cellular automata in real time, bridging a gap between sequential automata and cellular automata.

Findings

Simulation runs in real time, matching input length.

The automaton performs the same task as the original in linear time.

Raises questions about the equivalence of linear and real times in cellular automata.

Abstract

In this paper, we present the simulation of a simple, yet significantly powerful, sequential model by cellular automata. The simulated model is called oblivious multi-head one-way finite automata and is characterized by having its heads moving only forward, on a trajectory that only depends on the length of the input. While the original finite automaton works in linear time, its corresponding cellular automaton performs the same task in real time, that is, exactly the length of the input. Although not truly a speed-up, the simulation may be interesting and reminds us of the open question about the equivalence of linear and real times on cellular automata.