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Topological characterization of families of graphs generated by certain types of graph grammars

Mihalis Yannakakis, Theodosios Pavlidis
1979 Information and Control  
A precise topological characterization of classes of graphs generated by certain context free graph grammars (CFGG) is given, An informal interpretation of the results is that CFGG cannot generate any  ...  interesting classes of graphs besides trees and series-parallel networks, except in trivial ways (e.g. by including subgraphs of higher connectivity explicitly in the production rules).  ...  In Section 3 we consider general 2 a order context-free graph grammars and present certain characterizations for the families of graphs produced by them. II.  ... 
doi:10.1016/s0019-9958(79)90173-6 fatcat:23akzkkjwbdanetelxdwqpjynu

Linear and Context-Free Graph Grammars

T. Pavlidis
1972 Journal of the ACM  
Topological characterizations of sets of graphs which can be generated by contextfree or linear grammars are given.  ...  It is shown, for example, that the set of all planar graphs cannot be generated by a context-free grammar while the set of all outerplanar graphs can  ...  Topological Characterization of Graphs Generated by Coldext-Free Graph Grammars The type of a string grammar depends primarily on the size of patterns which can occur in the strings it generates.  ... 
doi:10.1145/321679.321682 fatcat:dpu4xl3tvvd5jm2gpw3xufuuka

Robust and Scalable Learning of Complex Intrinsic Dataset Geometry via ElPiGraph

Luca Albergante, Evgeny Mirkes, Jonathan Bac, Huidong Chen, Alexis Martin, Louis Faure, Emmanuel Barillot, Luca Pinello, Alexander Gorban, Andrei Zinovyev
2020 Entropy  
ElPiGraph exploits and further develops the concept of elastic energy, the topological graph grammar approach, and a gradient descent-like optimization of the graph topology.  ...  Multidimensional datapoint clouds representing large datasets are frequently characterized by non-trivial low-dimensional geometry and topology which can be recovered by unsupervised machine learning approaches  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/e22030296 pmid:33286070 pmcid:PMC7516753 fatcat:kdqf5e5zifgzzftgk4vkzsqqli

Page 2782 of Mathematical Reviews Vol. , Issue 80G [page]

1980 Mathematical Reviews  
Here the concepts of the generalized marking and the topological nets of marked functional graphs are introduced.  ...  “By the association of topology with marked functional graphs, some deeper ‘semantic’ analysis of marking processes is given.  ... 

Robust And Scalable Learning Of Complex Dataset Topologies Via Elpigraph [article]

Luca Albergante, Evgeny M. Mirkes, Huidong Chen, Alexis Martin, Louis Faure, Emmanuel Barillot, Luca Pinello, Alexander N. Gorban, Andrei Zinovyev
2018 arXiv   pre-print
This method is able to withstand high levels of noise and is capable of approximating complex topologies via principal graph ensembles that can be combined into a consensus principal graph.  ...  graph.  ...  This is possible because the local version of the elastic graph algorithm is characterized by certain persistency in choosing the direction of the graph growth.  ... 
arXiv:1804.07580v2 fatcat:va7y7s2x2vc2jc67bgbawlxhuu

Graph Grammar Based Product Family Modeling

Xuehong Du, Jianxin Jiao, Mitchell M. Tseng
2002 Concurrent Engineering - Research and Applications  
The paper introduces graph grammar formalisms to the modeling of such a product family.  ...  Based on Programmed Attributed Graph Grammars (PAGG), the graph language is developed to specify the design space of the product family.  ...  Graph Grammars for Product Family The term 'graph grammars' generally refers to a variety of methods for specifying (possibly infinite) sets of graphs (IWGG, 1987) .  ... 
doi:10.1177/1063293x02010002635 fatcat:4jkijrwysjggtnv7bnf6kbbome

Graph Structure and Monadic Second-Order Logic: Language Theoretical Aspects [chapter]

Bruno Courcelle
2008 Lecture Notes in Computer Science  
Graph structure is a flexible concept covering many different types of graph properties.  ...  Supported by the GRAAL project of "Agence Nationale pour la Recherche".  ...  Walukiewicz for many useful comments on a first draft of this overview. The first 11 references are books and survey articles.  ... 
doi:10.1007/978-3-540-70575-8_1 fatcat:ftpcqszcb5fs5nswbqnbnmy5ja

Page 1980 of Mathematical Reviews Vol. , Issue 80E [page]

1980 Mathematical Reviews  
Yannakakis, Mihalis; Pavlidis, Theodosios 80e:68174 Topological characterization of families of graphs generated by certain types of graph grammars.  ...  If the two graphs are generated by the same grammar, the distance is calculated by considering joint steps in the genesis of both graphs. The defined distance has the usual properties of a metric.  ... 

Reframing Decision Problems: A Graph-Grammar Approach

Shimon Schocken, Christopher Jones
1993 Information systems research  
The graph objects must be of certain types, and the graph topology must form a hierarchy, each node having at most one incoming edge.  ...  Edges of type echoice are characterized by a single l a b e l attribute, whereas edges of type echance are characterized by a l a b e l and a p r o b a b i l i t y attribute.  ...  Since the topology of the production takes care of all the necessary matchings, the indices associated with each of these edges match up automatically, and there is no need to write any explicit matching  ... 
doi:10.1287/isre.4.1.55 fatcat:z6oypk6jiva7fpubxdmfjvyauq

Combing Grammars and Space Syntax: Formulating, Generating and Evaluating Designs

Teresa V. Heitor, José P. Duarte, Rafaela M. Pinto
2004 International Journal of Architectural Computing  
Results suggest that space syntax is (1) useful in determining the universe of solutions generated by the grammar and (2) in evaluating the evolving designs in terms of spatial properties and, therefore  ...  , in guiding the generation of designs.  ...  In practical terms, space syntax would permit to characterize the adjacency graphs generated by Duarte's grammar in terms of those syntactic features.This would enable the discursive grammar to evaluate  ... 
doi:10.1260/1478077042906221 fatcat:b6wt4uzjhnhazkt7qupc2howha

Page 2094 of Mathematical Reviews Vol. , Issue 88d [page]

1988 Mathematical Reviews  
As in the case of locally testable languages, a theorem on graph congruences is used in order to obtain a characterization of the family of bilocally testable languages.  ...  Summary: “We give an algorithm which computes the set of de- scendants of a regular set R, for Thue systems of a certain type.  ... 

What symbolic dynamics do we get with a misplaced partition?

Erik M. Bollt, Theodore Stanford, Ying-Cheng Lai, Karol Życzkowski
2001 Physica D : Non-linear phenomena  
Therefore, we investigate consequences of using itineraries generated by a non-generating partition.  ...  In summary, we find the misrepresentation of the dynamical system by "sample-path" symbolic dynamics of an arbitrary partition can be severe, including (sometimes extremely) diminished topological entropy  ...  Acknowledgements EMB was supported by NSF under Grant Nos. DMS-9704639 and DMS-0071314. TBS was supported by NARC. YCL was supported by AFOSR under Grant No.  ... 
doi:10.1016/s0167-2789(01)00242-1 fatcat:qfkqepyw5vg6nn3eesrqkehsha

Minimum Spanning vs. Principal Trees for Structured Approximations of Multi-Dimensional Datasets

Alexander Chervov, Jonathan Bac, Andrei Zinovyev
2020 Entropy  
Such a method allows efficient comparison of graph-based data approximations of arbitrary topology and complexity.  ...  score the data cloud partitioning induced by the graphs.  ...  can be generated by a limited number of graph grammar operations.  ... 
doi:10.3390/e22111274 pmid:33287042 fatcat:owerah5ymfgavbxr74cqmlfjiq

Mesocopic comparison of complex networks based on periodic orbits

R. Stoop, J. Joller
2011 Chaos  
), leading to the conclusion that the observed grammar is very unlikely the product of chance.  ...  For a proof-of-concept, we consider Drosophila's precopulatory courtship, where our method reveals the existence of a complex grammar (similar to those found in complex physical systems and in language  ...  The thermodynamic formalism 8,11,12 systematically scans a family of measures by mimicking a "temperature" dependence of the matrix entries, by raising them to a power of b (the "inverse temperature").  ... 
doi:10.1063/1.3553643 pmid:21456854 fatcat:f464fce3p5bl3gh7dkrdvz2iha

Graph grammars with string-regulated rewriting

Daniel Lobo, Francisco J. Vico, Jürgen Dassow
2011 Theoretical Computer Science  
We give examples of the concept and compare its generative power to the power of the traditional context-free graph grammars.  ...  Accordingly, a graph derivation by the graph grammar resembles the developmental process of an organism.  ...  D.L. was supported in part by a research stay fellowship at Otto-von-Guericke-Universität Magdeburg from the Spanish Ministerio de Educación.  ... 
doi:10.1016/j.tcs.2011.07.004 fatcat:xrhxtxyedngnbevzba5szoo7tm
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