| Description |
1 online resource (475 pages) |
| 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; 1. Introduction; 2. Algebraic Specification of Concurrent Systems: An Example; 3. Simulation; 4. The Lattice of Simulation Congruences; 5. Models of Hierarchical Specifications; Acknowledgment; Appendix A. Basic Notions on Partial Algebras; References; Chapter 2. Characteristic Sets and Grobner Bases in Geometry Theorem Proving |
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1. An Introduction to the Methods2. Ritt's Characteristic Set Method; 3. Algebra and Geometry; 4. The Complete Method of Wu; 5. Geometry Theorem Proving Using the Grobner Basis Method; 6. A Comparison of the Two Methods; References; Chapter 3. On Recognizable Sets and Tree Automata; 1. Introduction; 2. Recognizable and Equational Sets: General Properties; 3. Recognizable Subsets of Free T-Magmas; 4. Various Notions of Trees; 5. Conclusion; Acknowledgements; References; Chapter 4. The Idea of a Diagram; 1. Grassmann Algebras; 2. Grassmann Geometry; 3. Equations; 4. Theorems; 5. Diagrams |
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6. Realizations7. Properties; 8. Proof; 9. Reduction; 10. Quantities; 11. Instantiation; 12. Inconclusive Proofs; 13. Coordinate Proofs; 14. Conclusion; Acknowledgements; References; Chapter 5. Rigid E-Unification and Its Applications to Equational Matings; 1. Introduction; 2. Preliminaries; 3. Preview of the Method; 4. Equational Matings; 5. A Skolem-Herbrand-Godel Theorem; 6. Complete Sets of Rigid E-Unifiers; 7. Minimal Rigid E-Unifiers; 8. The Reduction Procedure; 9. A Method for Finding Complete Sets of Rigid F-Unifiers; 10. Soundness, Completeness, and Decidability of the Method |
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11. NP-Completeness of Rigid E-Unification 12. Equational Applications of Rigid E-unification Matings; 13 A Refutation Procedure; 14. Conclusion and Further Work; Acknowledgement; References; Chapter 6. What Is Unification?; 1. Introduction; 2. Substitutions and Categories; 3. Equations and Solutions; 4. Types, Variables and Products; 5. Classical Term Substitution; 6. What Is Unification?; 7. Further Explorations; 8. Summary; References; Chapter 7. Some Fixpoint Techniques in Algebraic Structures and Applications to Computer Science; 1. Introduction; 2. Fixpoint Theorems; 3. Applications |
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4. Conclusion and DiscussionAcknowledgments; References; Chapter 8. Canonical Representatives for Observational Equivalence Classes; 1. Introduction; 2. Nondeterministic Measurement Systems; 3. Observing Concurrency Models; 4. Some Properties of Observational Equivalence; 5. Abstraction Homomorphisms; 6. Canonical Representatives; 7. Conclusion; Acknowledgements; References; Chapter 9. Minimizing Expansions of Recursions; 1. Introduction; 2. Expansions of IDB Predicates; 3. The A/V Graph and Branches; 4. Inter-Element Redundancy; 5. Intra-Element Redundancy; 6. Conclusion; Acknowledgement |
| Bibliography |
Includes bibliographical references and indexes |
| Notes |
Print version record |
| Subject |
Algebra, Abstract.
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Equations -- Numerical solutions.
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MATHEMATICS -- Algebra -- Intermediate.
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Algebra, Abstract
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Equations -- Numerical solutions
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| Form |
Electronic book
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| Author |
Aït-Kaci, Hassan, 1954-
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Nivat, M
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| ISBN |
9781483262475 |
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1483262472 |
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