## Language EquationsThe emphasis of the book is on introducing a unified theory of language equations and relations. Numerous techniques for solving different kinds of equations and relations are presented. The main objective is to obtain representations or constructions of the complete solution set of a given system of equations or relations. Typically, the constructions are effective only if the constant languages are regular. The book is readable by anyone with a working knowledge of elementary automata and language theory. There are numerous detailed examples as well as exercises that make this book suitable as a text for a graduate or an advanced undergraduate course. |

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### Contents

An Informal Introduction to Language Equations | 1 |

Basic Definitions | 10 |

Classical Language Equations and the Substitution Property | 21 |

Copyright | |

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### Common terms and phrases

A-property with respect algorithm arbitrary languages assume automata boolean automaton boolean language equations Chapter classical language equations complementation Consider the equation Consider the following consists of union constant languages construction context-free grammar context-free languages defined denotes derivatives determine deterministic finite automaton empty word EX^(CONST EX^(REG example exists a solution explicit language relations explicit relations finite automaton following system given system implicit equations implicit language equations infinitely many solutions Leiss Lemma maximal solution mixed system nondeterministic finite automata nonempty nonreturning normal form one-letter alphabet original system parametric representation problem Proof Proposition regular expressions regular languages regular solution respect to Xi Section solution exists solve structural induction subrelations subset superrelation system of equations system of implicit system of language two-sided language equations union and left-concatenation unique solution unrestricted concatenation variable Xi verify yields Z-test