Drags: A compositional algebraic framework for graph rewriting

Abstract We are interested in a natural generalization of term-rewriting techniques to what we call drags, viz. finite, directed, ordered, rooted multigraphs, each vertex of which is labeled by a function symbol. To this end, we develop a rich algebra of drags that generalizes the familiar term algebra and its associated rewriting capabilities. Viewing graphs as terms provides an initial building block for rewriting with such graphs, one that should impact the many areas where computations take place on graphs.

[1]  László Babai,et al.  Graph isomorphism in quasipolynomial time [extended abstract] , 2016, STOC.

[2]  J. Meseguer.  Rewriting as a unified model of concurrency , 1990, OOPSLA/ECOOP '90.

[3]  Hartmut Ehrig,et al.  Attributed graph transformation with inheritance: Efficient conflict detection and local confluence analysis using abstract critical pairs , 2012, Theor. Comput. Sci..

[4]  José Meseguer,et al.  Petri Nets Are Monoids , 1990, Inf. Comput..

[5]  Ernest J. H. Chang,et al.  An improved algorithm for decentralized extrema-finding in circular configurations of processes , 1979, CACM.

[6]  Hartmut Ehrig,et al.  Efficient Conflict Detection in Graph Transformation Systems by Essential Critical Pairs , 2008, Electron. Notes Theor. Comput. Sci..

[7]  Annegret Habel,et al.  Jungle evaluation , 1988, Fundam. Informaticae.

[8]  Jean Goubault-Larrecq,et al.  A Constructive Proof of the Topological Kruskal Theorem , 2013, MFCS.

[9]  Jean-Pierre Jouannaud,et al.  Church-Rosser Properties of Normal Rewriting , 2012, CSL.

[10]  Roberto Bruni,et al.  Normal forms for algebras of connection , 2002, Theor. Comput. Sci..

[11]  José Meseguer,et al.  Representation Theorems for Petri Nets , 1997, Foundations of Computer Science: Potential - Theory - Cognition.

[12]  Barbara König,et al.  Conditional Reactive Systems , 2011, FSTTCS.

[13]  Annegret Habel,et al.  Graph Unification and Matching , 1994, TAGT.

[14]  Ross Street,et al.  Traced monoidal categories , 1996 .

[15]  Zena M. Ariola,et al.  Equational Term Graph Rewriting , 1996, Fundam. Informaticae.

[16]  Hartmut Ehrig,et al.  Local Confluence for Rules with Nested Application Conditions , 2010, ICGT.

[17]  Bruno Courcelle.  Graph Rewriting: A Bibliographical Guide , 1993, Term Rewriting.

[18]  Hartmut Ehrig,et al.  Graph-Grammars: An Algebraic Approach , 1973, SWAT.

[19]  Nachum Dershowitz,et al.  Orderings for term-rewriting systems , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).

[20]  Wolfram Kahl.  Categories of Coalgebras with Monadic Homomorphisms , 2014, CMCS.

[21]  Fabio Gadducci,et al.  Confluence of Graph Rewriting with Interfaces , 2017, ESOP.

[22]  Hartmut Ehrig,et al.  Graph rewriting with unification and composition , 1986, Graph-Grammars and Their Application to Computer Science.

[23]  Annegret Habel,et al.  Unification, rewriting, and narrowing on term graphs , 1995, SEGRAGRA.

[24]  Yves Lafont,et al.  Interaction nets , 1989, POPL '90.

[25]  Annegret Habel,et al.  Double-Pushout Approach with Injective Matching , 1998, TAGT.

[26]  Jean-Claude Raoult,et al.  On graph rewritings , 1984, Bull. EATCS.

[27]  Hélène Kirchner,et al.  PORGY : a Visual Analytics Platform for System Modelling and Analysis Based on Graph Rewriting , 2017, EGC.

[28]  Vladimir Dotsenko,et al.  Algebraic Operads: An Algorithmic Companion , 2016 .

[29]  Zena M. Ariola,et al.  Cyclic lambda graph rewriting , 1994, Proceedings Ninth Annual IEEE Symposium on Logic in Computer Science.

[30]  Detlef Plump,et al.  Simplification Orders for Term Graph Rewriting , 1997, MFCS.

[31]  José Meseguer,et al.  On the Semantics of Petri Nets , 1992, CONCUR.

[32]  Lukasz Kaiser,et al.  Entanglement and the complexity of directed graphs , 2012, Theor. Comput. Sci..

[33]  Hélène Kirchner,et al.  Strategic port graph rewriting: an interactive modelling framework , 2018, Mathematical Structures in Computer Science.

[34]  Jean-Pierre Jouannaud,et al.  Rewrite Systems , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[35]  Hélène Kirchner,et al.  Completion of a Set of Rules Modulo a Set of Equations , 1986, SIAM J. Comput..

[36]  Bruno Courcelle,et al.  Graph Rewriting: An Algebraic and Logic Approach , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[37]  Masahito Hasegawa,et al.  Recursion from Cyclic Sharing: Traced Monoidal Categories and Models of Cyclic Lambda Calculi , 1997, TLCA.

[38]  Kristoffer Høgsbro Rose,et al.  Explicit Cyclic Substitutions , 1992, CTRS.

[39]  P. Selinger.  A Survey of Graphical Languages for Monoidal Categories , 2009, 0908.3347.

[40]  Bruno Guillaume,et al.  Non-simplifying Graph Rewriting Termination , 2013, TERMGRAPH.

[41]  Detlef Plump,et al.  Rooted Graph Programs , 2012, Electron. Commun. Eur. Assoc. Softw. Sci. Technol..

[42]  Jean-Pierre Jouannaud,et al.  Graph Path Orderings , 2018, LPAR.

[43]  Wolfgang Reisig.  Associative composition of components with double-sided interfaces , 2018, Acta Informatica.

[44]  Detlef Plump,et al.  Critical Pairs in Term Graph Rewriting , 1994, MFCS.

[45]  Martin Hofmann,et al.  Finite Dimensional Vector Spaces Are Complete for Traced Symmetric Monoidal Categories , 2008, Pillars of Computer Science.

[46]  J. Willems.  The Behavioral Approach to Open and Interconnected Systems , 2007, IEEE Control Systems.

[47]  Arend Rensink,et al.  A Tutorial on Graph Transformation , 2018, Graph Transformation, Specifications, and Nets.