Geodesic
Tree algebra of sofic tree languages
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 48 (2014) no. 4, pp. 431-451

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We consider the languages of finite trees called tree-shift languages which are factorial extensible tree languages. These languages are sets of factors of subshifts of infinite trees. We give effective syntactic characterizations of two classes of regular tree-shift languages: the finite type tree languages and the tree languages which are almost of finite type. Each class corresponds to a class of subshifts of trees which is invariant by conjugacy. For this goal, we define a tree algebra which is finer than the classical syntactic tree algebra based on contexts. This allows us to capture the notion of constant tree which is essential in the framework of tree-shift languages.

DOI : 10.1051/ita/2014018
Classification : 68501, 37B10
Keywords: symbolic dynamics, tree-shift, tree automata, tree algebra 
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     author = {Aubrun, Nathalie and B\'eal, Marie-Pierre},
     title = {Tree algebra of sofic tree languages},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {431--451},
     publisher = {EDP-Sciences},
     volume = {48},
     number = {4},
     year = {2014},
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Aubrun, Nathalie; Béal, Marie-Pierre. Tree algebra of sofic tree languages. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 48 (2014) no. 4, pp. 431-451. doi: 10.1051/ita/2014018

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