Geodesic
Alpha-matrix and graph-generated grammars
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 1 (2017), pp. 28-40

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In this paper we consider the extension of graph-generated grammars based on their matrix representations. We study two classes of graph-generated grammars associated with the vertex and edge marking of graphs. We define alpha-matrices over a semiring of languages specified by finite alphabet $\mathcal{A}$ and then define the corresponding matrix algebras. These concepts are then used for constructive representation of graph-generated languages and research of their equivalence. We define a matrix-generated grammars as a natural superclass of graph-generated grammars. All the proofs are illustrated by examples.
Keywords: semirings of languages, generative grammars, graph theory, paths in graphs, labeled graphs, graph-generated grammars, matrix-generated grammars.
Mots-clés : formal grammars 
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     author = {V. P. Tsvetov},
     title = {Alpha-matrix and graph-generated grammars},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {28--40},
     publisher = {mathdoc},
     number = {1},
     year = {2017},
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     url = {http://geodesic.mathdoc.fr/item/VSGU_2017_1_a3/}
}
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V. P. Tsvetov. Alpha-matrix and graph-generated grammars. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 1 (2017), pp. 28-40. http://geodesic.mathdoc.fr/item/VSGU_2017_1_a3/