Algebraic Techniques

Resolution of Equations in Algebraic Structures

Hassan Aït-Kaci, Maurice Nivat

• Publisher: Academic Press
• Year: 2014
• Print ISBN:
  9780120463701
• eBook ISBN:
  9781483262475
• Topic: Mathematics
• Subtopic: Algebra
• Index: Mathematics

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 lattice's maximum element Milner's 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.

Table of contents

• Front Cover
• Algebraic Techniques
• Copyright Page
• Table of Contents
• Contents of Volume 2: Rewriting Techniques
• Contributors
• Foreword
• A Preview of Volume 1: Algebraic Techniques
• Chapter 1. Bisimulation in Algebraic Specifications
• Chapter 2. Characteristic Sets and Gröbner Bases in Geometry Theorem Proving
• Chapter 3. On Recognizable Sets and Tree Automata
• Chapter 4. The Idea of a Diagram
• Chapter 5. Rigid E-Unification and Its Applications to Equational Matings
• Chapter 6. What Is Unification?
• Chapter 7. Some Fixpoint Techniques in Algebraic Structures and Applications to Computer Science
• Chapter 8. Canonical Representatives for Observational Equivalence Classes
• Chapter 9. Minimizing Expansions of Recursions
• Chapter 10. Tree Monoids and Recognizability of Sets of Finite Trees
• Chapter 11. Recursively Defined Types in Constructive Type Theory
• Chapter 12. Rule Transformation Methods in the Implementation of Logic Based Languages
• Index