حل معادلات در ساختارهای جبری، جلد اول: تکنیک‌های جبری

Resolution of Equations in Algebraic Structures: Volume 1, Algebraic Techniques is a collection of papers from the "Colloquium on Resolution of Equations in Algebraic Structures" held in Texas in May 1987. The papers discuss equations and algebraic structures relevant to symbolic computation and to the foundation of programming. One paper discusses the complete lattice of simulation congruences associated with the ground atomic theory of hierarchical specification, retrieving as the lattices maximum element Milners strong bisimulation for CCS. Another paper explains algebraic recognizability of subsets of free T-algebras, or equational theories, and covers discrete structures like those of words, terms, finite trees, and finite graphs. One paper proposes a general theory of unification using a category theoretic framework for various substitution systems including classical unification, E-unification, and order-sorted unification. Another paper shows the universality of algebraic equations in computer science. Fixpoint theorems in ordered algebraic structures can be applied in computer science. These theorems, or their variations, include semantics and proof theory, logic programming, as well as efficient strategies for answering recursive queries in deductive data bases. The collection is suitable for programmers, mathematicians, students, and instructors involved in computer science and computer technology. Content: Front Matter, Page iii Copyright, Page iv Contents of Volume 2: Rewriting Techniques, Page vii Contributors, Pages ix-x Foreword, Pages xi-xiii, Hassan Aït-Kaci, Maurice Nivat A Preview of Volume 1: Algebraic Techniques, Pages xv-xxi 1 - Bisimulation in Algebraic Specifications1, Pages 1-31, EGIDIO ASTESIANO, MARTIN WIRSING 2 - Characteristic Sets and Gröbner Bases in Geometry Theorem Proving, Pages 33-92, SHANG-CHING CHOU, WILLIAM F. SCHELTER, JIN-GEN YANG 3 - On Recognizable Sets and Tree Automata, Pages 93-126, B. COURCELLE 4 - The Idea of a Diagram, Pages 127-150, DESMOND FEARNLEY-SANDER 5 - Rigid E-Unification and, Its Applications to Equational Matings, Pages 151-216, JEAN GALLIER, WAYNE SNYDER, STAN RAATZ 6 - What Is Unification?: A Categorical View of Substitution, Equation and Solution, Pages 217-261, JOSEPH A. GOGUEN 7 - Some Fixpoint Techniques in Algebraic Structures and Applications to Computer Science, Pages 263-292, IRÈNE GUESSARIAN 8 - Canonical Representatives for Observational Equivalence Classes, Pages 293-319, UGO MONTANARI, MARCELLO SGAMMA 9 - Minimizing Expansions of Recursions, Pages 321-349, JEFFREY F. NAUGHTON, YEHOSHUA SAGIV 10 - Tree Monoids and Recognizability of Sets of Finite Trees, Pages 351-367, MAURICE NIVAT, ANDREAS PODELSKI 11 - Recursively Defined Types in Constructive Type Theory, Pages 369-410, PRAKASH PANANGADEN, PAUL MENDLER, MICHAEL I. SCHWARTZBACH 12 - Rule Transformation Methods in the Implementation of Logic Based Languages, Pages 411-444, DOMENICO SACCA, CARLO ZANIOLO Index, Pages 445-452