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Topological characterization of families of graphs generated by certain types of graph grammars
1979
Information and Control
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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
1972
Journal of the ACM
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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
2020
Entropy
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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
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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]
2018
arXiv
pre-print
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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
2002
Concurrent Engineering - Research and Applications
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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]
2008
Lecture Notes in Computer Science
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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
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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
1993
Information systems research
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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
2004
International Journal of Architectural Computing
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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
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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?
2001
Physica D : Non-linear phenomena
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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
2020
Entropy
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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
2011
Chaos
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), 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
2011
Theoretical Computer Science
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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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