Notes on Stack Machines and Quantum Stack Machines

TL;DR

This paper explores the relationships between multi-stack machines, classical automata, and quantum automata, providing clear definitions and demonstrating their equivalences and capabilities in recognizing various language classes.

Contribution

It offers a succinct, unified framework for defining multi-stack and quantum automata, clarifying their computational power and relationships to classical automata.

Findings

Pushdown automata are special cases of multi-stack machines.

Deterministic pushdown automata are equivalent to pushdown automata.

Quantum pushdown automata and quantum stack machines are formulated with concise definitions.

Abstract

Multi-stack machines and Turing machines can simulate to each other. In this note, we give a succinct definition of multi-stack machines, and from this definition it is clearly seen that pushdown automata and deterministic finite automata are special cases of multi-stack machines. Also, with this mode of definition, pushdown automata and deterministic pushdown automata are equivalent and recognize all context-free languages. In addition, we are motivated to formulate concise definitions of quantum pushdown automata and quantum stack machines.