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Language equations

Author: Ernst L Leiss
Publisher: New York : Springer, ©1999.
Series: Monographs in computer science.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:

Presenting a framework for a general theory for solving systems of equations and relations between languages, this book covers classical language equations, generalized derivatives, Boolean language  Read more...

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Additional Physical Format: Online version:
Leiss, Ernst L., 1952-
Language equations.
New York : Springer, ©1999
(OCoLC)654539861
Document Type: Book
All Authors / Contributors: Ernst L Leiss
ISBN: 038798626X 9780387986265
OCLC Number: 39732968
Description: xvi, 216 pages ; 24 cm.
Contents: 1.1 Arithmetic Equations 2 --
1.2 Language Equations 3 --
1.4 Nonlinear Equations 5 --
1.5 Invertibility of Operations 6 --
1.6 Implicit and Explicit Equations 6 --
1.8 Assumed Background of the Reader 9 --
2 Basic Definitions 10 --
2.1 The Alphabet 10 --
2.2 The Constant Languages 11 --
2.3 The Language Operations 11 --
2.4 The Variables 13 --
2.5 The Expressions 13 --
2.6 The Equations 15 --
2.6.1 Two-Sided Equations 16 --
2.6.2 Explicit and Implicit Equations 16 --
2.7 The Relations 17 --
3 Classical Language Equations and the Substitution Property 21 --
3.2 The Syntactic Solution Approach 23 --
3.3 The Substitution Property 28 --
3.4 Constructing Nondeterministic Finite Automata for the Solution Languages 31 --
3.5 A Note on Context-Free Grammars 34 --
4 Boolean Language Equations 38 --
4.1 Boolean Automata 39 --
4.2 The & lambda;-Property and the Normal Form Theorem 42 --
4.3 The Uniqueness Criterion for Boolean Equations 46 --
4.4 Generalized Derivatives of Expressions 47 --
4.5 Constructing a Boolean Automaton for the Solution of Boolean Equations 50 --
4.6 Boolean Equations with Multiple Solution 60 --
5 More on Generalized Derivatives 64 --
5.1 Derivatives and the & lambda;-Property 64 --
5.2 Existence and Uniqueness of Solutions 69 --
5.4 Techniques for Determining Whether a Word Is in a Solution 75 --
6 Star Equations 79 --
7 Explicit Equations over a One-Letter Alphabet 86 --
7.1 Properties of Languages over a One-Letter Alphabet 87 --
7.2 Normal Forms of Expressions Without Complementation 89 --
7.3 Two Key Theorems 91 --
7.4 Solving General Equations in One Variable 99 --
7.5 Solving Systems of Equations 101 --
7.6 Uniqueness and Regularity of Solutions 102 --
7.6.1 Uniqueness 102 --
7.6.2 Regularity 103 --
7.6.3 CFL over {a} 104 --
7.7 Explicit Equations over {a} with Complementation 105 --
8 Implicit Equations with Union and Left-Concatenation 109 --
8.1 Basic Properties of Implicit Language Equations 111 --
8.1.1 Existence of Solutions 111 --
8.1.2 Nonclosure of CFL Under Implicit Language Equations 112 --
8.2 A Procedure for Determining That No Solution Exists 114 --
8.3 Solving Implicit Language Equations 116 --
8.4 Characterizing Uniqueness in Implicit Language Equations 121 --
9 Regular Implicit Equations over a One-Letter Alphabet with Union, Concatenation, and Star 129 --
9.1 Properties of Expressions over a One-Letter Alphabet 130 --
9.2 Solving One Equation in One Variable 133 --
9.3 Solving Systems of Equations 136 --
9.4 Uniqueness of Solutions 140 --
10 Explicit Relations with Union and Left-Concatenation 146 --
10.2 Properties of Single Explicit Relations in One Variable 149 --
10.3 Solving Systems with Several Explicit Equations for One Variable 151 --
10.4 Solving Strictly Decoupled Systems 159 --
10.5 Solving General Decoupled Systems 162 --
11 Implicit Relations with Union and Left-Concatenation 171 --
11.1 Existence of Solutions 174 --
11.2 Uniqueness of Solutions 177 --
12 Two-Sided Language Equations 184 --
13 Mixed Systems 198 --
13.1 Mixed Systems of Equations with Union and Left-Concatenation 199 --
13.2 Mixed Systems of Equations over a One-Letter Alphabet with Regular Constants and Union, Concatenation, and Star 202 --
14 Open Problems 207 --
14.1 Classification 207 --
14.2 The Cardinality of the Alphabet 208 --
14.3 The Class of Constant Languages 209 --
14.4 The Set of Operations Involved 209 --
14.5 Two-Sided, Implicit, and Explicit Equations 210 --
14.6 Effectiveness of Constructions 211.
Series Title: Monographs in computer science.
Responsibility: Ernst L. Leiss.
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