One-Tape Turing Machine Variants and Language Recognition

TL;DR

This paper explores two restricted variants of one-tape Turing machines, called limited automata and strongly limited automata, and characterizes their capabilities in recognizing context-free languages, including deterministic subclasses.

Contribution

It introduces and analyzes strongly limited automata, showing their limitations compared to limited automata in recognizing deterministic context-free languages.

Findings

Limited automata characterize context-free languages.

Deterministic limited automata are equivalent to deterministic pushdown automata.

Deterministic strongly limited automata are less powerful than deterministic limited automata.

Abstract

We present two restricted versions of one-tape Turing machines. Both characterize the class of context-free languages. In the first version, proposed by Hibbard in 1967 and called limited automata, each tape cell can be rewritten only in the first $d$ visits, for a fixed constant $d\geq 2$. Furthermore, for $d=2$ deterministic limited automata are equivalent to deterministic pushdown automata, namely they characterize deterministic context-free languages. Further restricting the possible operations, we consider strongly limited automata. These models still characterize context-free languages. However, the deterministic version is less powerful than the deterministic version of limited automata. In fact, there exist deterministic context-free languages that are not accepted by any deterministic strongly limited automaton.