research-article

Open access

An inductive characterization of matching in binding bigraphs

Authors:

Troels C. Damgaard,

Arne J. Glenstrup,

Robin MilnerAuthors Info & Claims

Formal Aspects of Computing, Volume 25, Issue 2

Pages 257 - 288

https://doi.org/10.1007/s00165-011-0184-5

Published: 01 March 2013 Publication History

Abstract

We analyze the matching problem for bigraphs. In particular, we present a sound and complete inductive characterization of matching in bigraphs with binding. Our results yield a specification for a provably correct matching algorithm, as needed by our prototype tool implementing bigraphical reactive systems.

References

References

[1]

Birkedal L, Bundgaard M, Damgaard TC, Debois S, Elsborg E, Glenstrup AJ, Hildebrandt TT, Milner R, Niss H (2006) Bigraphical programming languages for pervasive computing. In: Strang T, Cahill V, Quigley A (eds) Proceedings of Pervasive 2006 International Workshop on Combining Theory and Systems Building in Pervasive Computing, pp 653–658

[2]

Birkedal L, Debois S, Elsborg E, Hildebrandt TT, Niss H (2006) Bigraphical models of context-aware systems. In: Aceto L, Ingólfsdóttir A (eds) Proceedings of the 9th International Conference on Foundations of Software Science and Computation Structure. Lecture Notes in Computer Science, vol 3921. Springer, Berlin, pp 187–201

[3]

Birkedal L, Damgaard TC, Glenstrup AJ, Milner R (2006) Matching of bigraphs. In: Proceedings of Graph Transformation for Verification and Concurrency Workshop 2006, Electronic Notes in Theoretical Computer Science. Elsevier, Amsterdam

[4]

Birkedal L, Debois S, Hildebrandt TT (2006) Sortings for reactive systems. In: Baier C, Hermanns H (eds) Proceedings of the 17th International Conference on Concurrency Theory. Lecture Notes in Computer Science, vol 4137. Springer, Berlin, pp 248–262

[5]

Damgaard TC (2006) Syntactic theory for bigraphs. Master’s thesis, IT University of Copenhagen

[6]

Damgaard TC and Birkedal L Axiomatizing binding bigraphs Nordic J Comput 2006 13 1–2 58-77

Digital Library

[7]

Ehrig H, Ehrig K, Prange U, Taentzer G (2006) Fundamentals of algebraic graph transformation. Monographs in theoretical computer science. An EATCS series. Springer, Berlin

[8]

Fu JJ Directed graph pattern matching and topological embedding J Algorithms 1997 22 2 372-391

Digital Library

[9]

Glenstrup AJ, Damgaard TC, Højsgaard E, Birkedal L (2010) An implementation of bigraph matching. Technical report TR-2010-135, IT University of Copenhagen

[10]

Jensen OH (2006) Mobile processes in bigraphs, monograph Available at. http://www.cl.cam.ac.uk/~rm135/Jensen-monograph.html

[11]

Jensen OH, Milner R (2004) Bigraphs and mobile processes (revised). Technical report UCAM-CL-TR-580, University of Cambridge

[12]

Leifer JJ, Milner R (2004) Transition systems, link graphs and Petri nets. Technical Report UCAM-CL-TR-598, University of Cambridge

[13]

Larrosa J and Valiente G Constraint satisfaction algorithms for graph pattern matching Math Struct Comput Sci 2002 12 403-422

Digital Library

[14]

Milner R (2004) Bigraphs whose names have multiple locality. Technical report UCAM-CL-TR-603, University of Cambridge

[15]

Milner R Axioms for bigraphical structure Math Struct Comput Sci 2005 15 6 1005-1032

Digital Library

[16]

Milner R Pure bigraphs: structure and dynamics Inform Comput 2006 204 1 60-122

[17]

Milner R The space and motion of communicating agents 2009 Cambridge Cambridge University Press

[18]

Selkow SM The tree-to-tree editing problem Inform Process Lett 1977 6 6 184-186

[19]

Shamir R and Tsur D Faster subtree isomorphism J Algorithms 1999 33 2 267-280

Digital Library

[20]

Ullman JD An algorithm for subgraph isomorphism J ACM 1976 23 1 31-42

Digital Library

[21]

Valiente G Algorithms on trees and graphs 2002 Berlin Springer

[22]

Varró G, Varró D, Friedl K (2005) Adaptive graph pattern matching for model transformations using model-sensitive search plans. In: Karsai G, Taentzer G (eds) GraMot 2005, International workshop on graph and model transformations. Electronic notes in theoretical computer science, pps 191–205

[23]

Zündorf A (1994) Graph pattern matching in PROGRES. In: Cuny JE, Ehrig H, Engels G, Rozenberg G (eds) TAGT, Lecture Notes in Computer Science, vol 1073. Springer, Berlin, pp 454–468

Cited By

Grzelak D(2024)BiGGer: A Model Transformation Tool written in Java for Bigraph Rewriting in GrGen.NETJournal of Open Source Software10.21105/joss.064919:98(6491)Online publication date: Jun-2024
https://doi.org/10.21105/joss.06491
Chiapperini AMiculan MPeressotti M(2022)Computing (optimal) embeddings of directed bigraphsScience of Computer Programming10.1016/j.scico.2022.102842221:COnline publication date: 1-Sep-2022
https://dl.acm.org/doi/10.1016/j.scico.2022.102842
Grzelak DAßmann U(2021)A Canonical String Encoding for Pure BigraphsSN Computer Science10.1007/s42979-021-00552-52:4Online publication date: 30-Apr-2021
https://dl.acm.org/doi/10.1007/s42979-021-00552-5
Show More Cited By

Index Terms

An inductive characterization of matching in binding bigraphs

Index terms have been assigned to the content through auto-classification.

Recommendations

Matching of Bigraphs

We analyze the matching problem for bigraphs. In particular, we present a sound and complete inductive characterization of matching of binding bigraphs. Our results pave the way for a provably correct matching algorithm, as needed for an implementation ...
Conditional Bigraphs
Graph Transformation
Abstract
Bigraphs are a universal graph based model, designed for analysing reactive systems that include spatial and non-spatial (e.g. communication) relationships. Bigraphs evolve over time using a rewriting framework that finds instances of a (sub)-...
Matching - A special case of unification?

Unification is the problem to solve equations of first order terms by finding (all) substitutions into their variables that make these two terms equal. Matching is the problem to solve equations, where only one of the terms has to be instantiated by the ...

Comments

Information & Contributors

Information

Published In

cover image Formal Aspects of Computing

Formal Aspects of Computing Volume 25, Issue 2

Mar 2013

182 pages

ISSN:0934-5043

EISSN:1433-299X

Issue’s Table of Contents

© British Computer Society 2011.

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 March 2013

Accepted: 27 May 2011

Revision received: 24 November 2010

Received: 12 February 2010

Published in FAC Volume 25, Issue 2

Author Tags

Qualifiers

Research-article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

8
Total Citations
View Citations
69
Total Downloads

Downloads (Last 12 months)46
Downloads (Last 6 weeks)8

Reflects downloads up to 23 Dec 2024

Other Metrics

View Author Metrics

Citations

Cited By

Grzelak D(2024)BiGGer: A Model Transformation Tool written in Java for Bigraph Rewriting in GrGen.NETJournal of Open Source Software10.21105/joss.064919:98(6491)Online publication date: Jun-2024
https://doi.org/10.21105/joss.06491
Chiapperini AMiculan MPeressotti M(2022)Computing (optimal) embeddings of directed bigraphsScience of Computer Programming10.1016/j.scico.2022.102842221:COnline publication date: 1-Sep-2022
https://dl.acm.org/doi/10.1016/j.scico.2022.102842
Grzelak DAßmann U(2021)A Canonical String Encoding for Pure BigraphsSN Computer Science10.1007/s42979-021-00552-52:4Online publication date: 30-Apr-2021
https://dl.acm.org/doi/10.1007/s42979-021-00552-5
Chiapperini AMiculan MPeressotti M(2020)Computing Embeddings of Directed BigraphsGraph Transformation10.1007/978-3-030-51372-6_3(38-56)Online publication date: 25-Jun-2020
https://dl.acm.org/doi/10.1007/978-3-030-51372-6_3
Gassara ABouassida Rodriguez IJmaiel MDrira K(2019)Executing bigraphical reactive systemsDiscrete Applied Mathematics10.1016/j.dam.2018.07.006253(73-92)Online publication date: Jan-2019
https://doi.org/10.1016/j.dam.2018.07.006
Gassara ABouassida IJmaiel MShin SShin DLencastre M(2017)A tool for modeling SoS architectures using bigraphsProceedings of the Symposium on Applied Computing10.1145/3019612.3019802(1787-1792)Online publication date: 3-Apr-2017
https://dl.acm.org/doi/10.1145/3019612.3019802
Xu DShi Q(2016)An Operable Matching Algorithm for Bigraphs2016 3rd International Conference on Information Science and Control Engineering (ICISCE)10.1109/ICISCE.2016.54(209-213)Online publication date: Jul-2016
https://doi.org/10.1109/ICISCE.2016.54
Bacci GMiculan MRizzi R(2014)Finding a Forest in a TreeTrustworthy Global Computing10.1007/978-3-662-45917-1_2(17-33)Online publication date: 23-Dec-2014
https://doi.org/10.1007/978-3-662-45917-1_2

View Options

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Article

Media

Figures

Other

Tables

View Issue’s Table of Contents