Notes on Stack Machines and Quantum Stack Machines

2025-11-21

AI Summary

Existing formal definitions of multi-stack automata and their quantum extensions lack unity and rigor. Method: We propose a compact, axiomatic model of multi-stack machines by reformulating state transitions and stack operations; we formally prove its Turing equivalence via simulation of Turing machines, and show that pushdown automata and deterministic finite automata arise as natural special cases; we further clarify the conditions under which nondeterministic and deterministic pushdown automata become equivalent within the multi-stack framework. Contribution/Results: We introduce quantum superposition and measurement into this model, defining quantum pushdown automata and quantum stack machines—the first unified framework capable of quantum recognition of context-free languages. This work establishes a foundational basis for quantum automata theory and quantum language recognition, bridging classical automata hierarchies with quantum computational models.

Technology Category

• Machine Learning: Quantum Machine Learning
• Knowledge Representation and Reasoning: Qualitative Reasoning
• Multiagent Systems: Other Foundations of Multi Agent Systems

Application Category

• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

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.

Problem

• Defining multi-stack machines and their computational equivalence
• Establishing relationships between automata types and stack machines
• Formulating concise definitions for quantum pushdown automata and stack machines

Innovation

• Defined multi-stack machines with succinct formalization
• Showed pushdown automata equivalence to deterministic versions
• Formulated concise definitions for quantum stack machines