Embeddings and Contexts for Link Graphs

Graph-rewriting has been a growing discipline for over three decades. It grew out of the study of graph grammars, in which – analogously to string and tree grammars – a principal interest was to describe the families of graphs that could be generated from a given set of productions. A fundamental contribution was, of course, the double-pushout construction of Ehrig and his colleagues [4]; it made precise how the left-hand side of a production, or rewriting rule, could be found to occur in a host graph, and how it should then be replaced by the right-hand side. This break-through led to many theoretical developments and many applications. It relies firmly upon the treatment of graphs as objects in a category whose arrows are embedding maps.

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

[2]  Robin Milner,et al.  Bigraphs and mobile processes (revised) , 2004 .

[3]  Luca Cardelli,et al.  Mobile Ambients , 1998, FoSSaCS.

[4]  C. A. R. Hoare,et al.  A Theory of Communicating Sequential Processes , 1984, JACM.

[5]  Robin Milner,et al.  Transition systems, link graphs and Petri nets , 2006, Mathematical Structures in Computer Science.

[6]  Robin Milner,et al.  Deriving Bisimulation Congruences for Reactive Systems , 2000, CONCUR.

[7]  Vladimiro Sassone,et al.  Deriving Bisimulation Congruences: A 2-categorical Approach , 2002, EXPRESS.

[8]  Hartmut Ehrig,et al.  Deriving Bisimulation Congruences in the DPO Approach to Graph Rewriting , 2004, FoSSaCS.

[9]  Robin Milner,et al.  Theories for the Global Ubiquitous Computer , 2004, FoSSaCS.

[10]  Robin Milner,et al.  Contexts and embeddings for closed shallow action graphs , 2000 .

[11]  Reiko Heckel,et al.  A Bi-Categorical Axiomatisation of Concurrent Graph Rewriting , 1999, CTCS.

[12]  Robin Milner,et al.  A Calculus of Communicating Systems , 1980, Lecture Notes in Computer Science.

[13]  Hartmut Ehrig,et al.  Bigraphs meet Double Pushouts , 2002, Bull. EATCS.

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

[15]  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.