
Confluent String Rewriting
Matthias Jantzen(Author)
Springer (Publisher)
Published on 5. October 2011
Book
Paperback/Softback
IX, 126 pages
978-3-642-64867-0 (ISBN)
Description
Replacement systems, such as term rewriting systems, tree manipulat ing systems, and graph grammars, have been used in Computer Science in the context of theorem proving, program optimization, abstract data types, algebraic simplification, and symbolic comput ation. Replacement systems for strings arose about seventy years earlier in the area of combinatory logic and group theory. The most natural and appropriate formalism for dealing with string rewriting is the notion of a semi-Thue system and this monograph treats its central aspects. The reduction relation is here defined firstly by the direction of the rules and secondly by some metric that yields efficient algorithms. These systems are general enough to discuss the basic notions of arbitrary replacement systems, such as termination, confluence, and the Church-Rosser property in its original meaning. Confluent semi-Thue systems in which each and every derivation consists of finitely many steps only are called complete; they guarantee the existence of unique normal forms as canonical representatives of the Thue congruence classes. Each such system can be considered a nondeterministic algorithm for the word problem which works correctly without backtracking. This is often conceptually simpler and more elegant than an ad hoc construction. In many cases a replace ment system can be altered to a complete system by the Knuth-Bendix completion method.
More details
Series
Edition
Softcover reprint of the original 1st ed. 1988
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Lower undergraduate
Illustrations
IX, 126 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 8 mm
Weight
224 gr
ISBN-13
978-3-642-64867-0 (9783642648670)
DOI
10.1007/978-3-642-61549-8
Schweitzer Classification
Other editions
Additional editions

Content
1. Basic Definitions.- 1.1 General Reduction Systems.- 1.2 String Rewriting.- 2. Decision Problems.- 2.1 Undecidability Results.- 2.2 Decidability Results.- 3. Congruential Languages Specified by Semi-Thue Systems.- 4. Complete STSs, Groups, and Monoids.- 4.1 Introduction and General Results.- 4.2 The STS S1 = {(abba, ?)}.- 5. The Special One-Relator STSs Snfor n > 1 and the Groups Gn.- 5.1 Definitions, Notation, and Characterization of Gnas a Semidirect Product.- 5.2 Matrix Representation of Gn in GL2(?).- 5.3 Normal Forms, Conjugates, and Homomorphisms.- 5.4 Commutativity and Unique Divisibility in Gn.- 5.5 Complete Presentation for Gn.- 5.6 Sn Has No Preperfect Equivalent.- 5.7 Irreducible Strings in STSs Equivalent to Sn.- References and Further Reading.