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74 changes: 37 additions & 37 deletions paper.bib
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Expand Up @@ -11,7 +11,7 @@ @book{heckel_GraphTransformationSoftware_2020
}

@book{steinberg_EMFEclipseModeling_2008,
title = {{{EMF}}: {{Eclipse Modeling Framework}}},
title = {{EMF}: Eclipse Modeling Framework},
shorttitle = {{{EMF}}},
author = {Steinberg, Dave and Budinsky, Frank and Paternostro, Marcelo},
date = {2008-12-16},
Expand Down Expand Up @@ -39,7 +39,7 @@ @incollection{konig_TutorialGraphTransformation_2018
}

@book{milner_SpaceMotionCommunicating_2009,
title = {The {{Space}} and {{Motion}} of {{Communicating Agents}}},
title = {The Space and Motion of Communicating Agents},
author = {Milner, Robin},
date = {2009},
edition = {1},
Expand Down Expand Up @@ -75,12 +75,12 @@ @inproceedings{leifer_DerivingBisimulationCongruences_2000
}

@incollection{milner_EmbeddingsContextsLink_2005,
title = {Embeddings and {{Contexts}} for {{Link Graphs}}},
booktitle = {Formal {{Methods}} in {{Software}} and {{Systems Modeling}}: {{Essays Dedicated}} to {{Hartmut Ehrig}} on the {{Occasion}} of {{His}} 60th {{Birthday}}},
title = {Embeddings and Contexts for Link Graphs},
booktitle = {Formal Methods in Software and Systems Modeling: Essays Dedicated to {{Hartmut Ehrig}} on the Occasion of His 60th Birthday},
author = {Milner, Robin},
editor = {Kreowski, Hans-Jörg and Montanari, Ugo and Orejas, Fernando and Rozenberg, Grzegorz and Taentzer, Gabriele},
date = {2005},
series = {Lecture {{Notes}} in {{Computer Science}}},
series = {Lecture Notes in Computer Science},
pages = {343--351},
publisher = {{Springer}},
location = {{Berlin, Heidelberg}},
Expand All @@ -91,21 +91,21 @@ @incollection{milner_EmbeddingsContextsLink_2005

@incollection{ehrig_BigraphsMeetDouble_2004,
title = {Bigraphs Meet Double Pushouts},
booktitle = {Current {{Trends}} in {{Theoretical Computer Science}}},
booktitle = {Current Trends in Theoretical Computer Science},
author = {Ehrig, Hartmut},
date = {2004-04-01},
pages = {27--40},
publisher = {{WORLD SCIENTIFIC}},
publisher = {World Scientific},
doi = {10.1142/9789812562494_0038},
isbn = {978-981-238-783-7},
volumes = {0}
}

@book{ehrig_FundamentalsAlgebraicGraph_2006,
title = {Fundamentals of {{Algebraic Graph Transformation}}},
title = {Fundamentals of Algebraic Graph Transformation},
author = {Ehrig, Hartmut and Ehrig, Karsten and Prange, Ulrike and Taentzer, Gabriele},
date = {2006},
series = {Monographs in {{Theoretical Computer Science}}. {{An EATCS Series}}},
series = {Monographs in Theoretical Computer Science. {A}n {EATCS} Series},
publisher = {{Springer-Verlag}},
location = {{Berlin Heidelberg}},
doi = {10.1007/3-540-31188-2},
Expand All @@ -114,12 +114,12 @@ @book{ehrig_FundamentalsAlgebraicGraph_2006
}

@inproceedings{chiapperini_ComputingEmbeddingsDirected_2020,
title = {Computing {{Embeddings}} of {{Directed Bigraphs}}},
booktitle = {Graph {{Transformation}}},
title = {Computing Embeddings of Directed Bigraphs},
booktitle = {Graph Transformation},
author = {Chiapperini, Alessio and Miculan, Marino and Peressotti, Marco},
editor = {Gadducci, Fabio and Kehrer, Timo},
date = {2020},
series = {Lecture {{Notes}} in {{Computer Science}}},
series = {Lecture Notes in Computer Science},
pages = {38--56},
publisher = {{Springer International Publishing}},
location = {{Cham}},
Expand All @@ -146,19 +146,19 @@ @report{grzelak_BigraphicalDomainspecificLanguage_2021
title = {Bigraphical Domain-specific Language (BDSL): User Manual},
author = {Grzelak, Dominik},
date = {2021-06-25},
institution = {{Technische Universität Dresden}},
institution = {Technische Universität Dresden},
url = {https://nbn-resolving.org/urn:nbn:de:bsz:14-qucosa2-752170},
langid = {german}
}

@inproceedings{geiss_GrGenFastSPOBased_2006,
title = {{{GrGen}}: {{A Fast SPO-Based Graph Rewriting Tool}}},
title = {{GrGen}: A Fast {SPO}-Based Graph Rewriting Tool},
shorttitle = {{{GrGen}}},
booktitle = {Graph {{Transformations}}},
booktitle = {Graph Transformations},
author = {Geiß, Rubino and Batz, Gernot Veit and Grund, Daniel and Hack, Sebastian and Szalkowski, Adam},
editor = {Corradini, Andrea and Ehrig, Hartmut and Montanari, Ugo and Ribeiro, Leila and Rozenberg, Grzegorz},
editor = {Corradini, Andrea and g, Hartmut and Montanari, Ugo and Ribeiro, Leila and Rozenberg, Grzegorz},
date = {2006},
series = {Lecture {{Notes}} in {{Computer Science}}},
series = {Lecture Notes in Computer Science},
pages = {383--397},
publisher = {{Springer Berlin Heidelberg}},
isbn = {978-3-540-38872-2},
Expand All @@ -167,30 +167,30 @@ @inproceedings{geiss_GrGenFastSPOBased_2006
}

@report{jakumeit_GrGenNETUser_2023,
title = {The {{GrGen}}.{{NET User Manual}}: {{Refers}} to {{GrGen}}.{{NET Release}} 6.7},
title = {The {GrGen.NET} User Manual: Refers to {GrGen.NET} Release 6.7},
author = {Jakumeit, Edgar and Blomer, Jakob and Geiß, Rubino},
date = {2023-05-18},
url = {https://www.grgen.de/GrGenNET-Manual.pdf},
langid = {english}
}
@inproceedings{varro_BenchmarkingGraphTransformation_2005,
title = {Benchmarking for {{Graph Transformation}}},
booktitle = {2005 {{IEEE Symposium}} on {{Visual Languages}} and {{Human-Centric Computing}} ({{VL}}/{{HCC}}'05)},
title = {Benchmarking for Graph Transformation},
booktitle = {2005 {IEEE} Symposium on Visual Languages and Human-Centric Computing ({VL/HCC}'05)},
author = {Varro, G. and Schurr, A. and Varro, D.},
date = {2005},
pages = {79--88},
publisher = {{IEEE}},
location = {{Dallas, TX, USA}},
doi = {10.1109/VLHCC.2005.23},
eventtitle = {2005 {{IEEE Symposium}} on {{Visual Languages}} and {{Human-Centric Computing}} ({{VL}}/{{HCC}}'05)},
eventtitle = {2005 {IEEE} Symposium on Visual Languages and Human-Centric Computing ({VL/HCC}'05)},
isbn = {978-0-7695-2443-6},
langid = {english}
}
@report{geiss_ImprovementsVarroBenchmark_2007,
title = {On Improvements of the {{Varró Benchmark}} for Graph Transformation Tools},
title = {On Improvements of the {V}arró Benchmark for Graph Transformation Tools},
author = {Geiß, Rubino and Kroll, Moritz},
date = {2007},
series = {Interner Bericht. {{Fakultät}} Für Informatik, Universität Karlsruhe},
series = {Interner Bericht. Fakultät Für Informatik, Universität Karlsruhe},
volume = {2007},
number = {7},
institution = {{Universität Karlsruhe (TH)}},
Expand All @@ -200,7 +200,7 @@ @report{geiss_ImprovementsVarroBenchmark_2007
}
@report{sevegnani_SATBasedAlgorithm_2010,
type = {Technical Report},
title = {A {{SAT}} Based Algorithm for the Matching Problem in Bigraphs with Sharing},
title = {A {SAT} Based Algorithm for the Matching Problem in Bigraphs with Sharing},
author = {Sevegnani, Michele and Unsworth, Chris and Calder, Muffy},
date = {2010},
number = {TR-2010-311},
Expand All @@ -219,16 +219,16 @@ @unpublished{miculan_CSPImplementationBigraph_2014
urldate = {2019-01-18}
}
@article{grzelak_BigraphEcoreMetamodel_2023,
title = {Bigraph {{Ecore Metamodel}} ({{BEM}}): {{An EMOF-Compliant Specification}} for {{Bigraphs}}},
shorttitle = {Bigraph {{Ecore Metamodel}} ({{BEM}})},
title = {Bigraph Ecore Metamodel ({BEM}): An {EMOF}-Compliant Specification for Bigraphs},
shorttitle = {Bigraph Ecore Metamodel ({BEM})},
author = {Grzelak, Dominik},
date = {2023-10-26},
publisher = {{Zenodo}},
url = {https://zenodo.org/records/10043063},
urldate = {2024-02-08}
}
@article{kehrer_EMOFCompliantAbstractSyntax_2016,
title = {An {{EMOF-Compliant Abstract Syntax}} for {{Bigraphs}}},
title = {An {EMOF}-Compliant Abstract Syntax for Bigraphs},
author = {Kehrer, Timo and Tsigkanos, Christos and Ghezzi, Carlo},
date = {2016-12-04},
journaltitle = {Electronic Proceedings in Theoretical Computer Science},
Expand All @@ -240,25 +240,25 @@ @article{kehrer_EMOFCompliantAbstractSyntax_2016
doi = {10.4204/EPTCS.231.2}
}
@inproceedings{bacci_FindingForestTree_2014,
title = {Finding a {{Forest}} in a {{Tree}}},
booktitle = {Trustworthy {{Global Computing}}},
title = {Finding a Forest in a Tree},
booktitle = {Trustworthy Global Computing},
author = {Bacci, Giorgio and Miculan, Marino and Rizzi, Romeo},
editor = {Maffei, Matteo and Tuosto, Emilio},
date = {2014},
series = {Lecture {{Notes}} in {{Computer Science}}},
series = {Lecture Notes in Computer Science},
pages = {17--33},
publisher = {{Springer Berlin Heidelberg}},
publisher = {Springer Berlin Heidelberg},
isbn = {978-3-662-45917-1},
langid = {english},
doi = {10.1007/978-3-662-45917-1_2}
}
@article{birkedal_MatchingBigraphs_2007,
title = {Matching of {{Bigraphs}}},
title = {Matching of Bigraphs},
author = {Birkedal, Lars and Damgaard, Troels Christoffer and Glenstrup, Arne John and Milner, Robin},
date = {2007-07-09},
journaltitle = {Electronic Notes in Theoretical Computer Science},
shortjournal = {Electronic Notes in Theoretical Computer Science},
series = {Proceedings of the {{Workshop}} on {{Graph Transformation}} for {{Concurrency}} and {{Verification}} ({{GT-VC}} 2006)},
series = {Proceedings of the Workshop on Graph Transformation for Concurrency and Verification {(GT-VC} 2006)},
volume = {175},
number = {4},
pages = {3--19},
Expand All @@ -279,9 +279,9 @@ @article{damgaard_InductiveCharacterizationMatching_2013
langid = {english}
}
@inproceedings{bacci_DBtkToolkitDirected_2009,
title = {{{DBtk}}: {{A Toolkit}} for {{Directed Bigraphs}}},
title = {DBtk: A Toolkit for Directed Bigraphs},
shorttitle = {{{DBtk}}},
booktitle = {Proceedings of the 3rd {{International Conference}} on {{Algebra}} and {{Coalgebra}} in {{Computer Science}}},
booktitle = {Proceedings of the 3rd International Conference on Algebra and Coalgebra in Computer Science},
author = {Bacci, Giorgio and Grohmann, Davide and Miculan, Marino},
date = {2009-09-07},
series = {{{CALCO}}'09},
Expand All @@ -294,9 +294,9 @@ @inproceedings{bacci_DBtkToolkitDirected_2009
doi = {10.1007/978-3-642-03741-2_28},
}
@inproceedings{sevegnani_BigraphERRewritingAnalysis_2016,
title = {{{BigraphER}}: {{Rewriting}} and {{Analysis Engine}} for {{Bigraphs}}},
title = {{BigraphER}: Rewriting and Analysis Engine for Bigraphs},
shorttitle = {{{BigraphER}}},
booktitle = {28th {{International Conference}} on {{Computer Aided Verification}}},
booktitle = {28th International Conference on Computer Aided Verification},
author = {Sevegnani, Michele and Calder, Muffy},
editor = {Chaudhuri, Swarat and Farzan, Azadeh},
date = {2016-07-17},
Expand Down
20 changes: 10 additions & 10 deletions paper.md
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Expand Up @@ -22,7 +22,7 @@ bibliography: paper.bib

# Summary

Graphs are well-studied mathematical structures that have diverse applications in fields such as computer science, chemistry, biology and social sciences.
Graphs are well-studied mathematical structures that have diverse applications in fields such as computer science, chemistry, biology, and social sciences.
In this respect, graph rewriting is a powerful technique that allows for the manipulation of graph structures through the application of so-called *graph transformation rules*.[^1]
In other words, graph rewriting techniques elevate static graphs to the concept of time-varying graphs.

Expand All @@ -40,7 +40,7 @@ Ultimately, this library transforms EMOF-complaint bigraphs into multigraphs tha
Furthermore, BiGGer is also shipped as a command-line tool for using the functionality via the terminal for experimentation.
The most challenging aspect was the accurate translation of bigraphical rules to SPO-based rules, given that bigraphs and GrGen.NET employ distinct approaches regarding graph rewriting.[^3]

[^3]: For an analysis of the interrelated aspects of these approaches, refer to [@milner_EmbeddingsContextsLink_2005; @ehrig_BigraphsMeetDouble_2004].
[^3]: For an analysis of the interrelated aspects of these approaches, refer to @milner_EmbeddingsContextsLink_2005 and @ehrig_BigraphsMeetDouble_2004.


# Statement of Need
Expand All @@ -53,23 +53,23 @@ The tool is built upon the formal principles of bigraphs, allowing for the intui

When considering the manipulation of bigraphs through rules, the central elements that require implementation are bigraph matching and rewriting.
This issue is mathematically known as the *subgraph isomorphism problem*, a general variant of the graph isomorphism problem.
Until now, it is unknown whether the test for graph isomorphism can be solved in polynomial time or whether it is NP-complete.
It is currently not known if the test for graph isomorphism can be solved in polynomial time or if it is NP-complete.
Subgraph isomorphism is computationally more complex than graph isomorphism and is known to be NP-complete due to the combinatorial nature of finding subpatterns in graphs.
Thus, graph rewriting is NP-complete [@bacci_FindingForestTree_2014].

However, bigraphs require the matching and rewriting of two substructures.
Specifically, one substructure of a bigraph is a *forest*, which is relevant to the problem of locating forests in trees [@bacci_FindingForestTree_2014], while the other substructure is a *hypergraph*, which is associated with the subhypergraph matching problem.
To date, practical bigraph matching primarily exists as a CSP implementation [@miculan_CSPImplementationBigraph_2014], or SAT-based algorithm [@sevegnani_SATBasedAlgorithm_2010] in the literature.

GrGen.NET provides a universal framework written in C# implementing the so-called Single-Pushout (SPO) approach of graph rewriting for multigraphs (see, for example, [@ehrig_FundamentalsAlgebraicGraph_2006; @jakumeit_GrGenNETUser_2023]).
The choice to use GrGen.NET instead of other common graph rewrite systems in the software domain (e.g., AGG, PROGRES, FUJABA) is its execution performance with respect to matching and rewriting (refer to the benchmark described in [@geiss_ImprovementsVarroBenchmark_2007], which was introduced in [@varro_BenchmarkingGraphTransformation_2005] first).
GrGen.NET provides a universal framework, written in C#, that implements the so-called Single-Pushout (SPO) approach of graph rewriting for multigraphs (see, for example, @ehrig_FundamentalsAlgebraicGraph_2006 and @jakumeit_GrGenNETUser_2023].
The choice to use GrGen.NET instead of other common graph rewrite systems in the software domain (e.g., AGG, PROGRES, FUJABA) is its execution performance with respect to matching and rewriting (refer to the benchmark described in @geiss_ImprovementsVarroBenchmark_2007, which was first introduced in @varro_BenchmarkingGraphTransformation_2005.)
Specifically, GrGen.NET's pattern matching engine employs some techniques that increase the practical execution performance of subgraph matching, which is an NP-complete problem but is at least one order of magnitude faster than comparable candidates [@jakumeit_GrGenNETUser_2023].

# Key Features

The tool implements a unidirectional transformation from bigraph models to GrGen.NET models, and generates several files that GrGen.NET can execute and visualize.
The tool implements a unidirectional transformation from bigraph models to GrGen.NET models and generates several files that GrGen.NET can execute and visualize.
These include GrGen.NET's graph metamodel (`*.gm`), the graph model conforming to the metamodel (`*.grs`), rules (`*.grg`), and a script that configures the initial graph state and defines a simple rule execution strategy (`*.grs`).
In turn this means that BiGGer is able to process the signature, bigraph, rules and tracking maps specified in the Eclipse EMF Ecore format [@steinberg_EMFEclipseModeling_2008], which implements the EMOF standard [@ISO19508_2014].
In turn this means that BiGGer is able to process the signature, bigraph, rules, and tracking maps specified in the Eclipse EMF Ecore format [@steinberg_EMFEclipseModeling_2008], which implements the EMOF standard [@ISO19508_2014].
Refer to [www.bigraphs.org](www.bigraphs.org) on how to model EMOF-compliant bigraphs in Java, visually or via the dedicated domain-specific language [@grzelak_BigraphicalDomainspecificLanguage_2021].

The functionality of BiGGer is offered via different interfaces suited for users of different backgrounds: programmatically in Java via the API, or by using the command-line tool.
Expand All @@ -81,10 +81,10 @@ Moreover, BiGGer is shipped with sample bigraphs and rules and detailed instruct
# [State of the Field\label{sec:StateoftheField}]()

There are few practical solutions concerned with the bigraph matching problem for various kinds of bigraphs; a non-exhaustive presentation is the following.
For *binding bigraphs* (i.e., links have local scopes) by an inductive characterization of matching [@birkedal_MatchingBigraphs_2007; @damgaard_InductiveCharacterizationMatching_2013]; for *directed bigraphs* (which subsume *pure bigraphs*) [@bacci_DBtkToolkitDirected_2009]; for \emph{bigraphs with sharing} (i.e., the place graph is a directed acyclic graph) by using a SAT-based algorithm [@sevegnani_BigraphERRewritingAnalysis_2016]; for the pure case by [@miculan_CSPImplementationBigraph_2014] as a CSP, and further an adapted reduction of the problem for directed bigraphs to a CSP [@chiapperini_ComputingEmbeddingsDirected_2020]; and the work in [@gassara_ExecutingBigraphicalReactive_2019], which proposes a toolchain for bigraph matching that is conceptually most similar to our approach but not actively developed anymore and not as efficient as GrGen.NET.
For *binding bigraphs* (i.e., links have local scopes) by an inductive characterization of matching [@birkedal_MatchingBigraphs_2007; @damgaard_InductiveCharacterizationMatching_2013]; for *directed bigraphs* (which subsume *pure bigraphs*) [@bacci_DBtkToolkitDirected_2009]; for \emph{bigraphs with sharing} (i.e., the place graph is a directed acyclic graph) by using a SAT-based algorithm [@sevegnani_BigraphERRewritingAnalysis_2016]; for the pure case by [@miculan_CSPImplementationBigraph_2014] as a CSP, and further an adapted reduction of the problem for directed bigraphs to a CSP [@chiapperini_ComputingEmbeddingsDirected_2020]; and the work in @gassara_ExecutingBigraphicalReactive_2019, which proposes a toolchain for bigraph matching that is conceptually most similar to our approach but not actively developed anymore and not as efficient as GrGen.NET.

# Acknowledgements

Funded by the German Research Foundation (DFG, Deutsche Forschungsgemeinschaft) as part of Germany’s Excellence Strategy – EXC 2050/1 – Project ID 390696704 – Cluster of Excellence "Centre for Tactile Internet with Human-in-the-Loop" (CeTI) of Technische Universität Dresden.
The work was funded by the German Research Foundation (DFG, Deutsche Forschungsgemeinschaft) as part of Germany’s Excellence Strategy – EXC 2050/1 – Project ID 390696704 – Cluster of Excellence "Centre for Tactile Internet with Human-in-the-Loop" (CeTI) of Technische Universität Dresden.

# References
# References

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