Word Equations And Related Topics

This volume contains papers presented at the first international workshop onword equations and related topics held at the University of T}bingen in October 1990. Word equations, the central topic of this annual workshop, lieat the intersection of several important areas of computer science, suchas unification theory, combinatorics on words, list processing, and constraint logic programming. The workshop is a forum where researchers fromthese different domains may present and discuss results and ideas, thereby supporting interaction and cross-fertilization between theoretical questions and practical applications. The volume collects papers which: - contain new and relevant results, - describe a new approach to a subject, or - give a survey of main developments in an area. Papers cover investigations on free groups, associative unification and Makanin's algorithm to decide the solvability of equations in free semigroups, general unification theory and its relationship to algebra and model theory, Thue systems, and finitely presented groups.

This volume contains papers presented at the second International Workshop on Word Equations and Related Topics (IWWERT '91), held at the University ofRouen in October 1991. The papers are on the following topics: general solution of word equations, conjugacy in free inverse monoids, general A- and AX-unification via optimized combination procedures, wordequations with two variables, a conjecture about conjugacy in free groups, acase of termination for associative unification, theorem proving by combinatorial optimization, solving string equations with constant restriction, LOP (toward a new implementation of Makanin's algorithm), word unification and transformation of generalizedequations, unification in the combination of disjoint theories, on the subsets of rank two in a free monoid (a fast decision algorithm), and a solution of the complement problem in associative-commutative theories.

A pattern is a word that consists of variables and terminal symbols. The pattern language that is generated by a pattern A is the set of all terminal words that can be obtained from A by uniform replacement of variables with terminal words. For example, the pattern A = xaxa (where x is a variable, and a is a terminal symbol) generates the set of all squares that end on a. Due to their simple definition, pattern languages have various connections to a wide range of other areas in computer science and mathematics. On the other hand, many of the canonical questions are surprisingly difficult for pattern languages. The present thesis discusses various aspects of the inclusion problem of pattern languages. It can be divided in two parts. The first one examines the decidability of the inclusion problem under various restrictions, and the related question of minimizability of regular expressions with repetition operators. The second part deals with descriptive patterns, the smallest generalizations of arbitrary languages through pattern languages ("smallest" with respect to the inclusion relation). Main topics are the existence and the discoverability of descriptive patterns.

This book constitutes the refereed proceedings of the 16th Annual Symposium on Theoretical Aspects of Computer Science, STACS 99, held in Trier, Germany in March 1999. The 51 revised full papers presented were selected from a total of 146 submissions. Also included are three invited papers. The volume is divided in topical sections on complexity, parallel algorithms, computational geometry, algorithms and data structures, automata and formal languages, verification, algorithmic learning, and logic in computer science.

The research results published in this book range from pure mathematical theory (semigroup theory, discrete mathematics, etc.) to theoretical computer science, in particular formal languages and automata. The papers address issues in the algebraic and combinatorial theories of semigroups, words and languages, the structure theory of automata, the classification theory of formal languages and codes, and applications of these theories to various areas, like quantum and molecular computing, coding theory, and cryptography.

The research results published in this book range from pure mathematical theory (semigroup theory, discrete mathematics, etc.) to theoretical computer science, in particular formal languages and automata. The papers address issues in the algebraic and combinatorial theories of semigroups, words and languages, the structure theory of automata, the classification theory of formal languages and codes, and applications of these theories to various areas, like quantum and molecular computing, coding theory, and cryptography. Contents: Semidirect Products with the Pseudovariety of All Finite Group (J Almeida & A Escada)On the Sentence Valuations in a Semiring (A Atanasiu et al.)Arithmetical Complexity of Infinite Words (S V Avgustinovich et al.)R-Trivial Languages of Words on Countable Ordinals (O Carton)Networks of Watson–Crick D0L Systems (E Csuhaj-Varjú & A Salomaa)On the Differentiation Function of Some Language Generating Devices (J Dassow)Quantum Finite Automata (J Gruska & R Vollmar)Error-Detecting Properties of Languages (S Konstantinidis)Power Semigroups and Polynomial Closure (S W Margolis & B Steinberg)Routes and Trajectories (A Mateescu)A Proof of Okninski and Putcha's Theorem (K Shoji)Tree Automata in the Theory of Term Rewriting (M Steinby)and other papers Readership: Computer scientists and mathematicians. Keywords: