A CSP implementation of the bigraph embedding problem

A crucial problem for many results and tools about bigraphs and bigraphical reactive systems is bigraph embedding. An embedding is more informative than a bigraph matching, since it keeps track of the correspondence between the various components of the redex (guest) within the agent (host). In this paper, we present an algorithm for computing embeddings based on a reduction to a constraint satisfaction problem. This algorithm, that we prove to be sound and complete, has been successfully implemented in LibBig, a library for manipulating bigraphical reactive systems. This library can be used for implementing a wide range of tools, and it can be adapted to various extensions of bigraphs.

[1]  Robin Milner,et al.  An inductive characterization of matching in binding bigraphs , 2013, Formal Aspects of Computing.

[2]  Espen Højsgaard.  Bigraphical Languages and their Simulation , 2011 .

[3]  Giorgio Bacci,et al.  On Decidability of Bigraphical Sorting , 2010 .

[4]  Marino Miculan,et al.  Bigraphs reloaded : a presheaf presentation , 2013 .

[5]  Laura Schweitzer.  The Space And Motion Of Communicating Agents , 2016 .

[6]  Thomas T. Hildebrandt,et al.  Formalizing Higher-Order Mobile Embedded Business Processes with Binding Bigraphs , 2008, COORDINATION.

[7]  Alessio Mansutti,et al.  Distributed execution of bigraphical reactive systems , 2015, Electron. Commun. Eur. Assoc. Softw. Sci. Technol..

[8]  Muffy Calder,et al.  Process Algebra for Event-Driven Runtime Verification: A Case Study of Wireless Network Management , 2012, IFM.

[9]  Jean Krivine,et al.  Formal Cellular Machinery , 2012, SASB.

[10]  John E. Hopcroft,et al.  Linear time algorithm for isomorphism of planar graphs (Preliminary Report) , 1974, STOC '74.

[11]  Giorgio Bacci,et al.  Bigraphical models for protein and membrane interactions , 2009, MeCBIC.

[12]  Thomas T. Hildebrandt,et al.  Big Red: A Development Environment for Bigraphs , 2013, Electron. Commun. Eur. Assoc. Softw. Sci. Technol..

[13]  Marino Miculan,et al.  Directed Bigraphs , 2007, MFPS.

[14]  Alessio Mansutti,et al.  Multi-agent Systems Design and Prototyping with Bigraphical Reactive Systems , 2014, DAIS.

[15]  Muffy Calder,et al.  A SAT based algorithm for the matching problem in bigraphs with sharing , 2010 .

[16]  Robert E. Tarjan,et al.  A V² Algorithm for Determining Isomorphism of Planar Graphs , 1971, Inf. Process. Lett..

[17]  Alan Bundy,et al.  Constructing Induction Rules for Deductive Synthesis Proofs , 2006, CLASE.

[18]  Søren Debois,et al.  Bigraphical Refinement , 2011, Refine@FM.

[19]  Hartmut Ehrig,et al.  Handbook of graph grammars and computing by graph transformation: vol. 3: concurrency, parallelism, and distribution , 1999 .

[20]  Christoph M. Kirsch,et al.  Bigactors — A model for structure-aware computation , 2013, 2013 ACM/IEEE International Conference on Cyber-Physical Systems (ICCPS).

[21]  Søren Debois,et al.  A model checker for Bigraphs , 2012, SAC '12.

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

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

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

[25]  Giorgio Bacci,et al.  Finding a Forest in a Tree - The Matching Problem for Wide Reactive Systems , 2014, TGC.