Universal Algebra and Applications in Theoretical Computer Science

Universal Algebra and Applications in Theoretical Computer Science

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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.show more

Product details

  • Hardback | 383 pages
  • 158.5 x 246.4 x 27.4mm | 743.9g
  • Taylor & Francis Inc
  • CRC Press Inc
  • Bosa Roca, United States
  • English
  • 40 black & white illustrations
  • 1584882549
  • 9781584882541

Table of contents

BASIC CONCEPTS Algebras Examples Subalgebras Congruence Relations and Quotients Exercises GALOIS CONNECTIONS AND CLOSURES Closure Operators Galois Connections Concept Analysis Exercises HOMOMORPHISMS AND ISOMORPHISMS The Homomorphism Theorem The Isomorphism Theorems Exercises DIRECT AND SUBDIRECT PRODUCTS Direct Products Subdirect Products Exercises TERMS, TREES, AND POLYNOMIALS Terms and Trees Term Operations Polynomials and Polynomial Operations Exercises IDENTITIES AND VARIETIES The Galois-Connection (Id, Mod) Fully Invariant Congruence Relations The Algebraic Consequence Relation Relatively Free Algebras Varieties The Lattice of All Varieties Finite Axiomatizability Exercises TERM REWRITING SYSTEMS Confluence Reduction Systems Term Rewriting Termination of Term Rewriting Systems Exercises ALGEBRAIC MACHINES Regular Languages Finite Automata Algebraic Operations on Finite Automata Tree-Recognizers Regular Tree Grammars Operations on Tree Languages Minimal Tree-Recognizers Tree Transducers Turing Machines Undecidable Problems Exercises MAL'CEV-TYPE CONDITIONS Congruence Permutability Congruence Distributivity Arithmetical Varieties n-Modularity and n-Permutability Congruence Regular Varieties Two-Element Algebras Exercises CLONES AND COMPLETENESS Clones as Algebraic Structures Operations and Relations The Lattice of all Boolean Clones The Functional Completeness Problem Primal Algebras Different Generalizations of Primality Preprimal Algebras TAME CONGRUENCE THEORY Minimal Algebras Tame Congruence Relations Permutation Algebras The Types of Minimal Algebras Mal'cev Conditions and Omitting Types Residually Small Varieties TERM CONDITION AND COMMUTATOR The Term Condition The Commutator COMPLETE SUBLATTICES Conjugate Pairs of Closure Operators Galois-Closed Subrelations Closure Operators on Complete Lattices G-CLONES AND M-SOLID VARIETIES G-Clones H-Clones M-Solid Varieties Intervals in the Lattice L(t) HYPERSUBSTITUTIONS AND MACHINES The Hyperunification Problem Hyper-Tree-Recognizers Tree Transformations BIBLIOGRAPHY INDEXshow more

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