Quantum logic and automata theory

Ying, M

Quantum logic and automata theory

Ying, M

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Publication Type:: Chapter
Citation:: Handbook of Quantum Logic and Quantum Structures, 2007, pp. 619 - 754
Issue Date:: 2007-12-01

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Field	Value	Language
dc.contributor.author	Ying, M https://orcid.org/0000-0003-4847-702X	en_US
dc.date.issued	2007-12-01	en_US
dc.identifier.citation	Handbook of Quantum Logic and Quantum Structures, 2007, pp. 619 - 754	en_US
dc.identifier.isbn	9780444528704	en_US
dc.identifier.uri	http://hdl.handle.net/10453/11648
dc.description.abstract	It is noted that a theory of computation based on quantum logic is to be established as a logical foundation of quantum computation. Finite automata and pushdown automata are considered the simplest abstract mathematical models of computing machines. Automata theory is an essential part of computation theory. This chapter describes a systematic exposition of automata theory. In context to this theory, quantum logic is treated as an orthomodular lattice-valued logic. The approach employed in developing this theory is essentially the semantical analysis. This chapter introduces notions of orthomodular lattice-valued finite automata and pushdown automata and their various variants. It defines the classes of languages accepted-namely, orthomodular lattice-valued regular languages and context-free languages. This chapter also re-examines various properties of automata in the framework of quantum logic, including the Kleene theorem concerning equivalence between finite automata and regular expressions, equivalence between pushdown automata and context-free grammars, and the pumping lemma both for regular languages and for context-free languages. © 2007 Copyright © 2007 Elsevier B.V. All rights reserved.	en_US
dc.relation.ispartof	Handbook of Quantum Logic and Quantum Structures	en_US
dc.relation.isbasedon	10.1016/B978-044452870-4/50037-6	en_US
dc.title	Quantum logic and automata theory	en_US
dc.type	Chapter
utslib.for	080199 Artificial Intelligence and Image Processing not elsewhere classified	en_US
utslib.for	080203 Computational Logic and Formal Languages	en_US
utslib.for	020603 Quantum Information, Computation and Communication	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Strength - QSI - Centre for Quantum Software and Information
utslib.copyright.status	closed_access
pubs.publication-status	Published	en_US

Abstract:

It is noted that a theory of computation based on quantum logic is to be established as a logical foundation of quantum computation. Finite automata and pushdown automata are considered the simplest abstract mathematical models of computing machines. Automata theory is an essential part of computation theory. This chapter describes a systematic exposition of automata theory. In context to this theory, quantum logic is treated as an orthomodular lattice-valued logic. The approach employed in developing this theory is essentially the semantical analysis. This chapter introduces notions of orthomodular lattice-valued finite automata and pushdown automata and their various variants. It defines the classes of languages accepted-namely, orthomodular lattice-valued regular languages and context-free languages. This chapter also re-examines various properties of automata in the framework of quantum logic, including the Kleene theorem concerning equivalence between finite automata and regular expressions, equivalence between pushdown automata and context-free grammars, and the pumping lemma both for regular languages and for context-free languages. © 2007 Copyright © 2007 Elsevier B.V. All rights reserved.

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http://hdl.handle.net/10453/11648