Computation in the Informatic Jungle

Informatics bridges Turing-computation and interactive behaviour; examples of the latter include ubiquitous/pervasive and biological systems. But how does a model of computation fit within a model of less disciplined informatic behaviour? This paper offers a precise treatment of that relationship, identifying a class of calculational bigraphical reactive systems. We show how such a system contains a confluent calculation sub-model, and how calculation only ever enables, never prevents, informatic behaviour of the larger model. We submit these results as a modest but essential beginning of a unified informatic theory.

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

[2]  Vijay A. Saraswat,et al.  Concurrent constraint programming , 1989, POPL '90.

[3]  Martín Abadi,et al.  A calculus for cryptographic protocols: the spi calculus , 1997, CCS '97.

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

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

[6]  Davide Sangiorgi,et al.  Communicating and Mobile Systems: the π-calculus, , 2000 .

[7]  Enno Ohlebusch,et al.  Term Rewriting Systems , 2002 .

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

[9]  Robin Milner,et al.  Axioms for bigraphical structure , 2005, Mathematical Structures in Computer Science.

[10]  Lars Birkedal,et al.  Sortings for Reactive Systems , 2006, CONCUR.

[11]  Vladimiro Sassone,et al.  Typed polyadic pi-calculus in bigraphs , 2006, PPDP '06.

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

[13]  Robin Milner,et al.  Local Bigraphs and Confluence: Two Conjectures: (Extended Abstract) , 2007, EXPRESS.

[14]  Robin Milner,et al.  Pure bigraphs: Structure and dynamics , 2006, Inf. Comput..

[15]  Lars Birkedal,et al.  Axiomatizing Binding Bigraphs , 2006, Nord. J. Comput..

[16]  Lars Birkedal,et al.  Bigraphical Models of Context-Aware Systems , 2006, FoSSaCS.

[17]  Marino Miculan,et al.  Reactive Systems over Directed Bigraphs , 2007, CONCUR.

[18]  Lars Birkedal,et al.  On the Construction of Sorted Reactive Systems , 2008, CONCUR.

[19]  Robin Milner,et al.  Stochastic Bigraphs , 2008, MFPS.

[20]  Robin Milner,et al.  The Space and Motion of Communicating Agents , 2009 .

[21]  Ebbe Elsborg,et al.  Bigraphs: Modelling, Simulation, and Type Systems On Bigraphs for Ubiquitous Computing and on Bigraphical Type Systems , 2009 .

[22]  Jakob Grue Simonsen,et al.  Least Upper Bounds on the Size of Church-Rosser Diagrams in Term Rewriting and λ-Calculus , 2010 .

[23]  Robin Milner,et al.  Unfolding CSP , 2010, Reflections on the Work of C. A. R. Hoare.