A CSP implementation of the directed bigraph embedding problem

Directed bigraphs are a meta-model which generalises Milner's bigraphs by taking into account the request flow between controls and names. A key problem about these bigraphs is that of bigraph embedding, i.e., finding the embeddings of a bigraph inside a larger one.We present an algorithm for computing embeddings of directed bigraphs, via a reduction to a constraint satisfaction problem. We prove soundness and completeness of this algorithm, and provide an implementation in jLibBig, a general Java library for manipulating bigraphical reactive systems, together with some experimental results.

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

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

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

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

[5]  Giorgio Bacci,et al.  A framework for protein and membrane interactions , 2009, MeCBIC.

[6]  Davide Grohmann.  Security, Cryptography and Directed Bigraphs , 2008, ICGT.

[7]  Marino Miculan,et al.  A CSP implementation of the bigraph embedding problem , 2014, ArXiv.

[8]  Mohamed Jmaiel,et al.  Executing bigraphical reactive systems , 2019, Discret. Appl. Math..

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

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

[11]  Éric Rutten,et al.  Modeling Self-adaptive Fog Systems Using Bigraphs , 2019, SEFM Workshops.

[12]  Marino Miculan,et al.  Controlling resource access in Directed Bigraphs , 2008, Electron. Commun. Eur. Assoc. Softw. Sci. Technol..

[13]  Giorgio Bacci,et al.  DBtk: A Toolkit for Directed Bigraphs , 2009, CALCO.

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

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

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

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

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

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

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

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

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

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

[24]  Marino Miculan,et al.  Towards a formal model for composable container systems , 2019, SAC.

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

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

[27]  Lars Birkedal,et al.  An Implementation of Bigraph Matching , 2008 .