Fundamentals of algebraic graph transformtion /

Fundamentals of algebraic graph transformtion /

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Bibliographic Details
Imprint:Berlin ; New York : Springer, c2006.
Description:xiii, 388 p. : ill. ; 24 cm.
Language:English
Series:Monographs in theoretical computer science
Subject:
Graph grammars.
Graph theory.
Morphisms (Mathematics)
Categories (Mathematics)
Categories (Mathematics)
Graph grammars.
Graph theory.
Morphisms (Mathematics)
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/5921303
Hidden Bibliographic Details
Other authors / contributors:Ehrig, Hartmut.
ISBN:3540311874
Notes:Includes bibliographical references (p. [377]-383) and index.
Standard no.:9783540311874
Table of Contents:
  • Part I. Introduction to Graph Transformation Systems
  • 1. General Introduction
  • 1.1. General Overview of Graph Grammars and Graph Transformation
  • 1.1.1. What Is Graph Transformation?
  • 1.1.2. Aims and Paradigms of Graph Transformation
  • 1.1.3. Overview of Various Approaches
  • 1.2. The Main Ideas of the Algebraic Graph Transformation Approach
  • 1.2.1. The DPO Approach
  • 1.2.2. The Algebraic Roots
  • 1.2.3. From the DPO to the SPO Approach
  • 1.2.4. From Graphs to High-Level Structures
  • 1.3. The Chapters of This Book and the Main Results
  • 1.3.1. Part I: Introduction to Graph Transformation Systems
  • 1.3.2. Part II: Adhesive HLR Categories and Systems
  • 1.3.3. Part III: Typed Attributed Graph Transformation Systems
  • 1.3.4. Part IV: Case Study and Tool Support
  • 1.3.5. Appendices
  • 1.3.6. Hints for Reading This Book
  • 1.4. Bibliographic Notes and Further Topics
  • 1.4.1. Concepts of Graph Grammars and Graph Transformation Systems
  • 1.4.2. Application Areas of Graph Transformation Systems
  • 1.4.3. Languages and Tools for Graph Transformation Systems
  • 1.4.4. Future Work
  • 2. Graphs, Typed Graphs, and the Gluing Construction
  • 2.1. Graphs and Typed Graphs
  • 2.2. Introduction to Categories
  • 2.3. Pushouts as a Gluing Construction
  • 2.4. Pullbacks as the Dual Construction of Pushouts
  • 3. Graph Transformation Systems
  • 3.1. Basic Definitions for GT Systems
  • 3.2. Construction of Graph Transformations
  • 3.3. Local Church-Rosser and Parallelism Theorems for GT Systems
  • 3.4. Overview of Some Other Main Results for GT Systems
  • 3.4.1. Concurrency Theorem
  • 3.4.2. Embedding and Extension Theorems
  • 3.4.3. Confluence, Local Confluence, Termination, and Critical Pairs
  • 3.4.4. Functional Behavior of GT Systems and Termination Analysis
  • 3.5. Graph Constraints and Application Conditions
  • Part II. Adhesive High-Level Replacement Categories and Systems
  • 4. Adhesive High-Level Replacement Categories
  • 4.1. Van Kampen Squares and Adhesive Categories
  • 4.2. Adhesive HLR Categories
  • 4.3. HLR Properties of Adhesive HLR Categories
  • 5. Adhesive High-Level Replacement Systems
  • 5.1. Basic Concepts of Adhesive HLR Systems
  • 5.2. Instantiation of Adhesive HLR Systems
  • 5.2.1. Graph and Typed Graph Transformation Systems
  • 5.2.2. Hypergraph Transformation Systems
  • 5.2.3. Petri Net Transformation Systems
  • 5.2.4. Algebraic Specification Transformation Systems
  • 5.2.5. Typed Attributed Graph Transformation Systems
  • 5.3. The Local Church-Rosser and Parallelism Theorems
  • 5.4. Concurrency Theorem and Pair Factorization
  • 6. Embedding and Local Confluence
  • 6.1. Initial Pushouts and the Gluing Condition
  • 6.2. Embedding and Extension Theorems
  • 6.3. Critical Pairs
  • 6.4. Local Confluence Theorem
  • 7. Constraints and Application Conditions
  • 7.1. Definition of Constraints and Application Conditions
  • 7.2. Construction of Application Conditions from Constraints
  • 7.3. Construction of Left from Right Application Conditions
  • 7.4. Guaranteeing and Preservation of Constraints
  • Part III. Typed Attributed Graph Transformation Systems
  • 8. Typed Attributed Graphs
  • 8.1. Attributed Graphs and Typing
  • 8.2. Pushouts as a Gluing Construction of Attributed Graphs
  • 8.3. Pullbacks of Attributed Graphs
  • 9. Typed Attributed Graph Transformation Systems
  • 9.1. Basic Concepts for Typed AGT Systems
  • 9.2. Construction of Typed Attributed Graph Transformations
  • 9.3. Local Church-Rosser and Parallelism Theorem for Typed AGT Systems
  • 9.4. Concurrency Theorem and Pair Factorization for Typed AGT Systems
  • 9.4.1. Pair Factorizations
  • 9.4.2. Concurrency Theorem
  • 10. Embedding and Local Confluence for Typed AGT Systems
  • 10.1. Embedding and Extension Theorems for Typed AGT Systems
  • 10.2. Critical Pairs for Typed AGT Systems
  • 10.3. Local Confluence Theorem for Typed AGT Systems
  • 11. Adhesive HLR Categories for Typed Attributed Graphs
  • 11.1. Attributed Graph Structure Signatures and Typed Attributed Graphs
  • 11.2. Definition of Concrete Adhesive HLR Categories
  • 11.3. Verification of the Main Results for Typed AGT Systems
  • 12. Constraints, Application Conditions and Termination for TAGT Systems
  • 12.1. Constraints and Application Conditions for Typed AGT Systems
  • 12.2. Equivalence of Constraints and Application Conditions
  • 12.3. Termination Criteria for Layered Typed Attributed Graph Grammars
  • 13. Typed Attributed Graph Transformation with Inheritance
  • 13.1. Attributed Type Graphs with Inheritance
  • 13.2. Attributed Clan Morphisms
  • 13.3. Productions and Attributed Graph Transformation with Inheritance
  • 13.4. Equivalence of Concepts with and without Inheritance
  • Part IV. Case Study on Model Transformation, and Tool Support by AGG
  • 14. Case Study on Model Transformation
  • 14.1. Model Transformation by Typed Attributed Graph Transformation
  • 14.2. Model Transformation from Statecharts to Petri Nets
  • 14.2.1. Source Modeling Language: Simple Version of UML Statecharts
  • 14.2.2. Target Modeling Language: Petri Nets
  • 14.2.3. Model Transformation
  • 14.2.4. Termination Analysis of the Model Transformation
  • 14.3. Further Case Studies
  • 14.3.1. From the General Resource Model to Petri Nets
  • 14.3.2. From Process Interaction Diagrams to Timed Petri Nets
  • 14.4. Conclusion
  • 15. Implementation of Typed Attributed Graph Transformation by AGG
  • 15.1. Language Concepts of AGG
  • 15.1.1. Graphs
  • 15.1.2. Typing Facilities
  • 15.1.3. Node and Edge Attributes
  • 15.1.4. Rules and Matches
  • 15.1.5. Graph Transformations
  • 15.1.6. Graph Grammars
  • 15.2. Analysis Techniques Implemented in AGG
  • 15.2.1. Graph Constraints
  • 15.2.2. Critical Pair Analysis
  • 15.2.3. Graph Parsing
  • 15.2.4. Termination
  • 15.3. Tool Environment of AGG
  • 15.3.1. Visual Environment
  • 15.3.2. Graph Transformation Engine
  • 15.3.3. Tool Integration
  • 15.4. Conclusion
  • Appendices
  • A. A Short Introduction to Category Theory
  • A.1. Categories
  • A.2. Construction of Categories, and Duality
  • A.3. Monomorphisms, Epimorphisms, and Isomorphisms
  • A.4. Pushouts and Pullbacks
  • A.5. Binary Coproducts and Initial Objects
  • A.6. Functors, Functor Categories, and Comma Categories
  • A.7. Isomorphism and Equivalence of Categories
  • B. A Short Introduction to Signatures and Algebras
  • B.1. Algebraic Signatures
  • B.2. Algebras
  • B.3. Terms and Term Evaluation
  • C. Detailed Proofs
  • C.1. Completion of Proof of Fact 4.24
  • C.2. Proof of Lemma 6.25
  • C.3. Completion of Proof of Theorem 11.3
  • C.3.1. Well-Definedness
  • C.3.2. Functors
  • C.3.3. Isomorphism
  • C.4. Proof of Lemma 11.17
  • C.4.1. Well-Definedness
  • C.4.2. Pushout Property
  • C.4.3. Initial Pushout
  • C.5. Proof of Theorem 13.12
  • C.6. Proof of Lemma 13.20
  • References
  • Index
Gift of Belle Friedman bookplate

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