Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Notes on Stack Machines and Quantum Stack Machines

Daowen Qiu

TL;DR

This note gives 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.

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.

Notes on Stack Machines and Quantum Stack Machines

TL;DR

This note gives 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.

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.

Paper Structure

This paper contains 5 theorems, 25 equations, 3 figures.

Key Result

lemma 1

Hop79 Let $\Sigma$ be a finite alphabet. For any language $L\subseteq \Sigma^*$, then $L$ is a context-free language if and only of $L$ is recognized by a pushdown automaton-I.

Figures (3)

  • Figure 1: Two-stack machine $M(L_{eq})$ recognizes $L_{eq}$.
  • Figure 2: Two-stack machine $M(L_{w})$ recognizes $L_{w}$.
  • Figure 3: PDA-II $M(L_{wwr})$ recognizes $L_{wwr}$.

Theorems & Definitions (17)

  • definition 1
  • definition 2
  • definition 3
  • definition 4
  • lemma 1
  • definition 5
  • definition 6
  • lemma 2
  • theorem 1
  • proof
  • ...and 7 more