Algebraic Techniques

Algebraic Techniques

Resolution of Equations in Algebraic Structures

1st Edition - June 28, 1989

Write a review

  • Editors: Hassan Aït-Kaci, Maurice Nivat
  • eBook ISBN: 9781483262475

Purchase options

Purchase options
DRM-free (PDF)
Sales tax will be calculated at check-out

Institutional Subscription

Free Global Shipping
No minimum order


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

  • Contents of Volume 2: Rewriting Techniques



    Α Preview of Volume 1: Algebraic Techniques

    1 Bisimulation in Algebraic Specifications

    2 Characteristic Sets and Gröbner Bases in Geometry Theorem Proving

    3 On Recognizable Sets and Tree Automata

    4 The Idea of a Diagram

    5 Rigid E-Unification and Its Applications to Equational Matings

    6 What Is Unification?

    7 Some Fixpoint Techniques in Algebraic Structures and Applications to Computer Science

    8 Canonical Representatives for Observational Equivalence Classes

    9 Minimizing Expansions of Recursions

    10 Tree Monoids and Recognizability of Sets of Finite Trees

    11 Recursively Defined Types in Constructive Type Theory

    12 Rule Transfomation Methods in the Implementation of Logic Based Languages


Product details

  • No. of pages: 474
  • Language: English
  • Copyright: © Academic Press 1989
  • Published: June 28, 1989
  • Imprint: Academic Press
  • eBook ISBN: 9781483262475

About the Editors

Hassan Aït-Kaci

Maurice Nivat

Ratings and Reviews

Write a review

There are currently no reviews for "Algebraic Techniques"