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

1979
*
Information and Control
*

A precise

doi:10.1016/s0019-9958(79)90173-6
fatcat:23akzkkjwbdanetelxdwqpjynu
*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. ...##
###
Linear and Context-Free Graph Grammars

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*. ...

##
###
Robust and Scalable Learning of Complex Intrinsic Dataset Geometry via ElPiGraph

2020
*
Entropy
*

ElPiGraph exploits and further develops the concept

doi:10.3390/e22030296
pmid:33286070
pmcid:PMC7516753
fatcat:kdqf5e5zifgzzftgk4vkzsqqli
*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. ...##
###
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]

2018
*
arXiv
*
pre-print

This method is able to withstand high levels

arXiv:1804.07580v2
fatcat:va7y7s2x2vc2jc67bgbawlxhuu
*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. ...##
###
Graph Grammar Based Product Family Modeling

2002
*
Concurrent Engineering - Research and Applications
*

The paper introduces

doi:10.1177/1063293x02010002635
fatcat:4jkijrwysjggtnv7bnf6kbbome
*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) . ...##
###
Graph Structure and Monadic Second-Order Logic: Language Theoretical Aspects
[chapter]

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. ...

##
###
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

1993
*
Information systems research
*

The

doi:10.1287/isre.4.1.55
fatcat:z6oypk6jiva7fpubxdmfjvyauq
*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 ...##
###
Combing Grammars and Space Syntax: Formulating, Generating and Evaluating Designs

2004
*
International Journal of Architectural Computing
*

Results suggest that space syntax is (1) useful in determining the universe

doi:10.1260/1478077042906221
fatcat:b6wt4uzjhnhazkt7qupc2howha
*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 ...##
###
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?

2001
*
Physica D : Non-linear phenomena
*

Therefore, we investigate consequences

doi:10.1016/s0167-2789(01)00242-1
fatcat:qfkqepyw5vg6nn3eesrqkehsha
*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. ...##
###
Minimum Spanning vs. Principal Trees for Structured Approximations of Multi-Dimensional Datasets

2020
*
Entropy
*

Such a method allows efficient comparison

doi:10.3390/e22111274
pmid:33287042
fatcat:owerah5ymfgavbxr74cqmlfjiq
*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. ...##
###
Mesocopic comparison of complex networks based on periodic orbits

2011
*
Chaos
*

), leading to the conclusion that the observed

doi:10.1063/1.3553643
pmid:21456854
fatcat:f464fce3p5bl3gh7dkrdvz2iha
*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"). ...##
###
Graph grammars with string-regulated rewriting

2011
*
Theoretical Computer Science
*

We give examples

doi:10.1016/j.tcs.2011.07.004
fatcat:xrhxtxyedngnbevzba5szoo7tm
*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. ...
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