ABSTRACT

Over the past 20 years, the emergence of clone theory, hyperequational theory, commutator theory and tame congruence theory has led to a growth of universal algebra both in richness and in applications, especially in computer science. Yet most of the classic books on the subject are long out of print and, to date, no other book has integrated these theories with the long-established work that supports them.

Universal Algebra and Applications in Theoretical Computer Science introduces the basic concepts of universal algebra and surveys some of the newer developments in the field. The first half of the book provides a solid grounding in the core material. A leisurely pace, careful exposition, numerous examples, and exercises combine to form an introduction to the subject ideal for beginning graduate students or researchers from other areas. The second half of the book focuses on applications in theoretical computer science and advanced topics, including Mal'cev conditions, tame congruence theory, clones, and commutators.

The impact of the advances in universal algebra on computer science is just beginning to be realized, and the field will undoubtedly continue to grow and mature. Universal Algebra and Applications in Theoretical Computer Science forms an outstanding text and offers a unique opportunity to build the foundation needed for further developments in its theory and in its computer science applications.

chapter 1|24 pages

Basic Concepts

chapter |6 pages

n02 is a congruence relation on

chapter 2|1 pages

Galois Connections and Closures

chapter 2|3 pages

1 Closure Operators

chapter |7 pages

n8 c c(n8) C(nB) B, n5

chapter 2|5 pages

3 Concept Analysis

chapter 3|16 pages

Homomorphisms and Isomorphisms

chapter 4|7 pages

Direct and Subdirect Products

chapter |1 pages

Aj -+

chapter |1 pages

[49,

H (A1613

chapter |3 pages

n{ConA\

chapter 5|1 pages

Terms, Trees, and Polynomials

chapter 5|13 pages

1 Terms and Trees

chapter |2 pages

:I'M

chapter 6|24 pages

Identities and Varieties

chapter 7|3 pages

Term Rewriting Systems

chapter |8 pages

, AA

chapter 7|7 pages

TERM REWRITING SYSTEMS

chapter |11 pages

REWRITING

chapter |3 pages

fo of weight

chapter 8|3 pages

Algebraic Machines

chapter 8|9 pages

2 Finite Automata

chapter 8|15 pages

3 Algebraic Operations on Finite Automata

chapter 8|4 pages

6 Operations on Tree Languages

chapter |15 pages

U {el

chapter 9|22 pages

Mal'cev-Type Conditions

chapter 10|2 pages

Clones and Completeness

chapter 10|34 pages

2 Operations and Relations

chapter 11|38 pages

Tame Congruence Theory

chapter 12|12 pages

Term Condition and Commutator

chapter 13|3 pages

Complete Sublattices

chapter |12 pages

') by(s) = t('r2(s)), (s) i(s),

(id) -ri(t-r(s)) = t-r(s), (iv')

chapter 13|9 pages

3 Closure Operators on Complete Lattices

chapter 14|2 pages

G-Clones and M-Solid Varieties

chapter |2 pages

g c SA

chapter |18 pages

g is a subgroup of g', gCg' C OP),

chapter 15|5 pages

7 The Hyperunification Problem

chapter |3 pages

= fe2

chapter |2 pages

(o-Ar[t] = 41-

chapter 15|6 pages

9 Tree Transformations