A Relation-Algebraic Approach to Graph Structure Transformation

Graph transformation is a rapidly expanding field of research, motivated by a wide range of applications.

[1]  Daniel J. Dougherty,et al.  Normal Forms and Reduction for Theories of Binary Relations , 2000, RTA.

[2]  J. Riguet,et al.  Relations binaires, fermetures, correspondances de Galois , 1948 .

[3]  A Fibred Approach to Rewriting | How the Duality between Adding and Deleting Cooperates with the Diierence between Matching and Rewriting , 1997 .

[4]  Gunther Schmidt,et al.  Programs as Partial Graphs I: Flow Equivalence and Correctness , 1981, Theor. Comput. Sci..

[5]  William Kneale.  ON THE SYLLOGISM AND OTHER LOGICAL WRITINGS , 1966 .

[6]  H. Ehrig,et al.  The ESPRIT Basic Research Working Group COMPUGRAPH "Computing by Graph Transformation": A Survey , 1993, Theor. Comput. Sci..

[7]  Albert Zündorf,et al.  The PROGRES approach: language and environment , 1999 .

[8]  J. Michael Spivey,et al.  The Z notation - a reference manual , 1992, Prentice Hall International Series in Computer Science.

[9]  M. Minas,et al.  Application of graph transformation to visual languages , 1999 .

[10]  Hans Zierer,et al.  Relation Algebraic Domain Constructions , 1991, Theor. Comput. Sci..

[11]  Grzegorz Rozenberg,et al.  Handbook of Graph Grammars and Computing by Graph Transformations, Volume 1: Foundations , 1997 .

[12]  Rod M. Burstall,et al.  Computational category theory , 1988, Prentice Hall International Series in Computer Science.

[13]  P. Burmeister.  A Model Theoretic Oriented Approach to Partial Algebras , 1986 .

[14]  Berthold Hoffmann,et al.  Hierarchical Graph Transformation , 2002, J. Comput. Syst. Sci..

[15]  Annegret Habel,et al.  Hyperedge Replacement, Graph Grammars , 1997, Handbook of Graph Grammars.

[16]  Richard Kennaway.  On "On Graph Rewritings" , 1987, Theor. Comput. Sci..

[17]  Alfred Tarski,et al.  Relational selves as self-affirmational resources , 2008 .

[18]  A. Lindenmayer,et al.  GROWING CELLULAR SYSTEMS: GENERATION OF GRAPHS BY PARALLEL REWRITING , 1979 .

[19]  Marko C. J. D. van Eekelen,et al.  Functional Programming and Parallel Graph Rewriting , 1993 .

[20]  Roger D. Maddux.  The derivation of identities involving projection functions , 1993 .

[21]  Christopher V. Jones,et al.  An Introduction to Graph-Based Modeling Systems, Part I: Overview , 1990, INFORMS J. Comput..

[22]  Andrea Corradini,et al.  Hyperedge Replacement Jungle Rewriting for Term-Rewriting Systems and Programming , 1993, Theor. Comput. Sci..

[23]  Reiko Heckel,et al.  A Combined Reference Model- and View-Based Approach to System Specification , 1997, Int. J. Softw. Eng. Knowl. Eng..

[24]  Erik Barendsen,et al.  Graph rewriting aspects of functional programming , 1999 .

[25]  Jules Desharnais,et al.  Monomorphic Characterization of n-ary Direct Products , 1999, Inf. Sci..

[26]  Gunther Schmidt,et al.  Relations and Graphs: Discrete Mathematics for Computer Scientists , 1993 .

[27]  Reiko Heckel,et al.  Algebraic Approaches to Graph Transformation - Part I: Basic Concepts and Double Pushout Approach , 1997, Handbook of Graph Grammars.

[28]  Michal Walicki,et al.  Categories of relational structures , 1997, WADT.

[29]  A. Carboni,et al.  Cartesian bicategories I , 1987 .

[30]  Peter Padawitz,et al.  Graph Grammars and Operational Semantics , 1978, Theor. Comput. Sci..

[31]  Yasuo Kawahara.  Pushout-Complements and Basic Concepts of Grammars in Toposes , 1990, Theor. Comput. Sci..

[32]  Hartmut Ehrig,et al.  From Graph Grammars to High Level Replacement Systems , 1990, Graph-Grammars and Their Application to Computer Science.

[33]  Michel Bauderon.  Parallel rewriting of graphs through the pullback approach , 1995, Electron. Notes Theor. Comput. Sci..

[34]  Michel Bauderon.  Categorical product as a genericgraph rewriting mechanism ? , 1996 .

[35]  Hans-Jörg Kreowski,et al.  Is parallelism already concurrency? Part 1: Derivations in graph grammars , 1986, Graph-Grammars and Their Application to Computer Science.

[36]  C. Siegel.  Vorlesungen über die Algebra der Logik , 1907 .

[37]  Hartmut Ehrig,et al.  Theory and application of graph transformations : 6th International Workshop, TAGT '98, Paderborn, Germany, November 16-20, 1998 : selected papers , 2000 .

[38]  Berthold Hoffmann,et al.  Implementing term rewriting by jungle evaluation , 1991, RAIRO Theor. Informatics Appl..

[39]  Reiko Heckel,et al.  Algebraic Approaches to Graph Transformation - Part II: Single Pushout Approach and Comparison with Double Pushout Approach , 1997, Handbook of Graph Grammars.

[40]  Richard Banach.  Term Graph Rewriting and Garbage Collection Using Ppfibrations , 1994, Theor. Comput. Sci..

[41]  Wolfram Kahl,et al.  A Study on Symmetric Quotients , 1998 .

[42]  Joan Torrens,et al.  Algebraic Transformation of Unary Partial Algebras I: Double-Pushout Approach , 1997, Theor. Comput. Sci..

[43]  Hélène Jacquet.  Une approche catégorique de la réécriture des sommets dans les graphes , 1999 .

[44]  D. A. Waller,et al.  Kronecker Products and Local Joins of Graphs , 1977, Canadian Journal of Mathematics.

[45]  Hélène Jacquet,et al.  Node Replacement in Hypergraphs: Translating NCE Rewriting into the Pullback Approach , 1998, TAGT.

[46]  Yasuo Kawahara,et al.  NOTES ON THE UNIVERSALITY OF RELATIONAL FUNCTORS , 1973 .

[47]  Roland Carl Backhouse,et al.  A relational theory of datatypes , 1992 .

[48]  Willem P. de Roever,et al.  Data Refinement: Model-oriented Proof Theories and their Comparison , 1998, Cambridge Tracts in Theoretical Computer Science.

[49]  Francesco Parisi-Presicce.  Single vs. Double Pushout Derivations of Graphs , 1992, WG.

[50]  Hartmut Ehrig,et al.  Graph Transformations in Computer Science , 1994, Lecture Notes in Computer Science.

[51]  F. W. Lawvere,et al.  FUNCTORIAL SEMANTICS OF ALGEBRAIC THEORIES. , 1963, Proceedings of the National Academy of Sciences of the United States of America.

[52]  Reiko Heckel,et al.  Open graph transformation systems: a new approach to the compositional modelling of concurrent and reactive systems , 1998 .

[53]  Przemyslaw Prusinkiewicz,et al.  The Algorithmic Beauty of Plants , 1990, The Virtual Laboratory.

[54]  Michael Barr,et al.  Category theory for computing science , 1995, Prentice Hall International Series in Computer Science.

[55]  Yasuo Kawahara,et al.  Kyushu University Institutional Repository Categorical Representation Theorems of Fuzzy Relations , 2022 .

[56]  S. Vickers.  Topology via Logic , 1989 .

[57]  Daniel J. Dougherty,et al.  The arithmetic and geometry of allegories: normal forms and complexity of a fragment of the theory of relations , 1999 .

[58]  Jules Desharnais,et al.  Refinement and Demonic Semantics , 1997, Relational Methods in Computer Science.

[59]  Frank Wolter,et al.  On Logics with Coimplication , 1998, J. Philos. Log..

[60]  Gunther Schmidt,et al.  Symmetric Quotients and Domain Constructions , 1989, Inf. Process. Lett..

[61]  George Gratzer,et al.  Universal Algebra , 1979 .

[62]  B. Jónsson.  Topics in universal algebra , 1972 .

[63]  Chris Jones.  Attributed graphs, graph-grammars, and Structured Modeling , 1992, Ann. Oper. Res..

[64]  Hartmut Ehrig,et al.  Tutorial Introduction to the Algebraic Approach of Graph Grammars Based on Double and Single Pushouts , 1990, Graph-Grammars and Their Application to Computer Science.

[65]  Detlef Plump,et al.  Term graph rewriting , 1999 .

[66]  Richard Kennaway,et al.  Graph Rewriting in Some Categories of Partial Morphisms , 1990, Graph-Grammars and Their Application to Computer Science.

[67]  Michel Bauderon,et al.  A Uniform Approach to Graph Rewriting: The Pullback Approach , 1995, WG.

[68]  Michel Bauderon,et al.  Pullback as a Generic Graph Rewriting Mechanism , 2001, Appl. Categorical Struct..

[69]  Yasuo Kawahara,et al.  RELATIONS IN CATEGORIES WITH PULLBACKS , 1973 .

[70]  Hartmut Ehrig,et al.  Algebraic Approach to Graph Transformation Based on Single Pushout Derivations , 1991, WG.

[71]  Dany Serrato,et al.  Squares and rectangles in relation categories. Three cases: semilattice, distributive lattice and Boolean non-unitary , 1995 .

[72]  Rudolf Berghammer,et al.  Relational Algebraic Semantics of Deterministic and Nondeterministic Programs , 1986, Theor. Comput. Sci..

[73]  Hans Zierer.  Programmierung mit Funktionsobjekten: konstruktive Erzeugung semantischer Bereiche und Anwendung auf die partielle Auswertung , 1988 .

[74]  Yasuo Kawahara,et al.  MATRIX CALCULUS IN I-CATEGORIES AND AN AXIOMATIC CHARACTERIZATION OF RELATIONS IN A REGULAR CATEGORY , 1973 .

[75]  A. Schfürr,et al.  Programmed graph replacement systems , 1997 .

[76]  Hans Jürgen Schneider,et al.  Describing Distributed Systems by Categorical Graph Grammars , 1989, WG.

[77]  J. Cuny.  Graph Gramars and Their Application to Computer Science, 5th International Workshop, Williamsburg, VA, USA, November 13-18, 1994, Selected Papers , 1996, TAGT.

[78]  Manfred Nagl,et al.  Graph-Grammars and Their Application to Computer Science , 1986, Lecture Notes in Computer Science.

[79]  Joost Engelfriet,et al.  Node Replacement Graph Grammars , 1997, Handbook of Graph Grammars.

[80]  Michael Winter,et al.  Heterogeneous Relation Algebra , 1997, Relational Methods in Computer Science.

[81]  Azriel Rosenfeld,et al.  Web Grammars , 1969, IJCAI.

[82]  Michel Bauderon,et al.  Node Rewriting in Hypergraphs , 1996, WG.

[83]  Wolfram Kahl,et al.  Algebraische Termgraphersetzung mit gebundenen Variablen , 1996, Informatik.

[84]  Annegret Habel,et al.  Amalgamation of Graph Transformations with Applications to Synchronization , 1985, TAPSOFT, Vol.1.

[85]  Martin Odersky,et al.  Abstract State Machines - Theory and Applications , 2002, Lecture Notes in Computer Science.

[86]  Christopher V. Jones.  An Introduction to Graph-Based Modeling Systems, Part II: Graph-Grammars and the Implementation , 1991, INFORMS J. Comput..

[87]  Hartmut Ehrig,et al.  Handbook of graph grammars and computing by graph transformation: vol. 2: applications, languages, and tools , 1999 .

[88]  Gunther Schmidt,et al.  Relation algebras: Concept of points and representability , 1985, Discret. Math..

[89]  Hartmut Ehrig,et al.  Introduction to the Algebraic Theory of Graph Grammars (A Survey) , 1978, Graph-Grammars and Their Application to Computer Science and Biology.

[90]  Carsten Butz,et al.  Finitely Presented Heyting Algebras , 1998 .

[91]  Hartmut Ehrig,et al.  Fundamentals of Algebraic Specification 1 , 1985, EATCS Monographs on Theoretical Computer Science.

[92]  H. Ehrig,et al.  Loose Semantics and Constraints for Graph Transformation Systems , 1997 .

[93]  Azriel Rosenfeld,et al.  Graph Grammars and Their Application to Computer Science , 1990, Lecture Notes in Computer Science.

[94]  A. Tarski,et al.  A Formalization Of Set Theory Without Variables , 1987 .

[95]  Hitoshi Furusawa,et al.  Algebraic Formalisations of Fuzzy Relations and Their Representation Theorems , 1997 .

[96]  M. Barr,et al.  Toposes, Triples and Theories , 1984 .

[97]  Roland Carl Backhouse,et al.  Programs and Datatypes , 1997, Relational Methods in Computer Science.

[98]  Martin Gogolla,et al.  Defining Operational Behavior of Object Specifications by Attributed Graph Transformations , 1996, Fundam. Informaticae.

[99]  Wolfram Kahl,et al.  Relational Methods in Computer Science , 1997, Advances in Computing Sciences.

[100]  Martin Gogolla,et al.  Semantics of object-oriented languages , 1999 .

[101]  Hartmut Ehrig,et al.  Graph-Grammars and Their Application to Computer Science and Biology , 1978, Lecture Notes in Computer Science.

[102]  Hans-Jörg Kreowski,et al.  Is parallelism already concurrency? Part 2: Non-sequential processes in graph grammars , 1986, Graph-Grammars and Their Application to Computer Science.

[103]  D. Monk.  On representable relation algebras. , 1964 .

[104]  Gunther Schmidt,et al.  Relationen und Graphen , 1989, Mathematik für Informatiker.

[105]  Wolfram Kahl.  Relational Matching for Graphical Calculi of Relations , 1999, Inf. Sci..

[106]  Hartmut Ehrig,et al.  Graph-Grammars: An Algebraic Approach , 1973, SWAT.

[107]  Annegret Habel,et al.  Double-pushout graph transformation revisited , 2001, Mathematical Structures in Computer Science.

[108]  Gunther Schmidt,et al.  Programs as Partial Graphs II: Recursion , 1981, Theor. Comput. Sci..

[109]  Manfred Nagl,et al.  Applications of Graph Transformations with Industrial Relevance , 2004, Lecture Notes in Computer Science.