Zigzags in Turing machines

TL;DR

This paper explores the dynamics of one-head Turing machines by linking their movement patterns to symbolic and topological dynamics, focusing on recognition complexity and automaton classes.

Contribution

It characterizes the class of one-head machines recognizable by deterministic pushdown automata through dynamical restrictions and equicontinuity.

Findings

Recognition complexity relates to head movement restrictions.

Deterministic pushdown automaton recognition corresponds to equicontinuity.

Specific dynamical restrictions characterize automaton recognizability.

Abstract

We study one-head machines through symbolic and topological dynamics. In particular, a subshift is associated to the subshift, and we are interested in its complexity in terms of realtime recognition. We emphasize the class of one-head machines whose subshift can be recognized by a deterministic pushdown automaton. We prove that this class corresponds to particular restrictions on the head movement, and to equicontinuity in associated dynamical systems.