Axioms for bigraphical structure

This paper axiomatises the structure of bigraphs, and proves that the resulting theory is complete. Bigraphs are graphs with double structure, representing locality and connectivity. They have been shown to represent dynamic theories for the $\pi$-calculus, mobile ambients and Petri nets in a way that is faithful to each of those models of discrete behaviour. While the main purpose of bigraphs is to understand mobile systems, a prerequisite for this understanding is a well-behaved theory of the structure of states in such systems. The algebra of bigraph structure is surprisingly simple, as this paper demonstrates; this is because bigraphs treat locality and connectivity orthogonally.

[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]  Peter Sewell,et al.  From Rewrite to Bisimulation Congruences , 1998, CONCUR.

[3]  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.

[4]  José Meseguer,et al.  Petri Nets Are Monoids , 1990, Inf. Comput..

[5]  Corrado Priami,et al.  Application of a stochastic name-passing calculus to representation and simulation of molecular processes , 2001, Inf. Process. Lett..

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

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

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

[9]  Robin Milner,et al.  Bigraphs for Petri Nets , 2003, Lectures on Concurrency and Petri Nets.

[10]  Robin Milner,et al.  Communication and concurrency , 1989, PHI Series in computer science.

[11]  Robin Milner,et al.  Bigraphical reactive systems: basic theory , 2001 .

[12]  Robin Milner,et al.  Bigraphs and transitions , 2003, POPL '03.

[13]  R. Milner.  Calculi for interaction , 1996, Acta Informatica.

[14]  Peter Sewell,et al.  From rewrite rules to bisimulation congruences , 2002, Theor. Comput. Sci..

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

[16]  R. Milner,et al.  Bigraphical Reactive Systems , 2001, CONCUR.

[17]  Philippa Gardner,et al.  From Process Calculi to Process Frameworks , 2000, CONCUR.

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

[19]  Robin Milner,et al.  A Calculus of Mobile Processes, II , 1992, Inf. Comput..

[20]  Robin Milner,et al.  A Calculus of Mobile Processes, II , 1992, Inf. Comput..

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

[22]  Luca Cardelli,et al.  BioAmbients: an abstraction for biological compartments , 2004, Theor. Comput. Sci..

[23]  David B. Benson.  The Basic Algebraic Structures in Categories of Derivations , 1975, Inf. Control..

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

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

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

[27]  James J. Leifer,et al.  Operational congruences for reactive systems , 2001 .