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Tree algebra of sofic tree languages∗

Published online by Cambridge University Press:  11 August 2014

Nathalie Aubrun  and
Marie–Pierre Béal
Nathalie Aubrun
Affiliation:
LIP, UMR 5668, ENS de Lyon, CNRS, France.. [email protected]
Marie–Pierre Béal
Affiliation:
Université Paris-Est, Laboratoire d’informatique Gaspard-Monge, UMR 8049 CNRS, France.; [email protected]
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Abstract

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.

Keywords

Symbolic dynamicstree-shifttree automatatree algebra
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 48 , Issue 4: Special issue in the honor of the 14th "Journées Montoises d'Informatique Théorique" , October 2014 , pp. 431 - 451
Copyright
© EDP Sciences 2014

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References

N. Aubrun and M.-P. Béal, Decidability of conjugacy of tree-shifts of finite type. In ICALP ’09: Proc. of the 36th International Colloquium on Automata, Languages and Programming. Springer-Verlag Berlin, Heidelberg (2009) 132–143.
N. Aubrun and M.-P. Béal, Sofic and almost of finite type tree-shifts. In 5th International Computer Science Symposium in Russia, (CSR’10), edited by E. Mayr and F. Ablayev, number 6072 in Lect. Notes Comput. Sci. Springer-Verlag (2010) 12–24.
Aubrun, N. and Béal, M.-P., Tree-shifts of finite type. Theoret. Comput. Sci. 459 (2012) 16–25. Google Scholar
Aubrun, N. and Béal, M.-P., Sofic tree-shifts. Theory Comput. Syst. 53 (2013) 621–644. Google Scholar
Béal, M.-P., Fiorenzi, F. and Perrin, D., A hierarchy of shift equivalent sofic shifts. Theoret. Comput. Sci. 345 (2005) 190–205. Google Scholar
M. Bojanczyk, Algebra for Trees. In Handbook of Automata Theory. To appear in EMS Publishing.
M. Bojanczyk, Effective characterizations of tree logics. Tutorial at PODS 2008 (2008).
M. Bojanczyk, L. Segoufin and H. Straubing, Piecewise testable tree languages. In LICS (2008) 442–451.
Boyle, M., Kitchens, B. and Marcus, B., A note on minimal covers for sofic systems. Proc. Amer. Math. Soc. 95 (1985) 403–411. Google Scholar
T. Ceccherini–Silberstein, M. Coornaert, F. Fiorenzi and Z. Sunic, Cellular automata on regular rooted trees. In CIAA 2012 (2012) 101–112.
H. Comon, M. Dauchet, R. Gilleron, C. Löding, F. Jacquemard, D. Lugiez, S. Tison and M. Tommasi, Tree automata techniques and applications. Available on: http://www.grappa.univ-lille3.fr/tata, release October, 12th (2007).
de Luca, A. and Restivo, A., A characterization of strictly locally testable languages and its applications to subsemigroups of a free semigroup. Inform. Control 44 (1980) 300–319. Google Scholar
G. Fici and F. Fiorenzi, Topological properties of cellular automata on trees. In DCM (2012) 255–266.
Heuter, U., Definite tree languages. Bulletin of the EATCS 35 (1988) 137–142. Google Scholar
U. Heuter, Generalized definite tree languages. In Mathematical Foundations of Computer Science 1989 (Pora¸bka-Kozubnik, 1989), vol. 379 of Lect. Notes Comput. Sci. Springer, Berlin (1989) 270–280.
E. Jeandel and G. Theyssier, Subshifts, languages and logic. In Developments in Language Theory, 13th International Conference, DLT 2009, Stuttgart, Germany, June 30 - July 3, 2009. Proceedings, vol. 5583 of Lect. Notes Comput. Sci. Springer (2009).
D. Lind and B. Marcus, An Introduction to Symbolic Dynamics and Coding. Cambridge University Press, Cambridge (1995).
Nivat, M. and Podelski, A., Definite tree languages. Bulletin of the EATCS 38 (1989) 186–190. Google Scholar
T. Place and L. Segoufin, A decidable characterization of locally testable tree languages. In ICALP (2), Lect. Notes Comput. Sci. Springer (2009) 285–296.
S. Salehi, A completeness property of wilke’s tree algebras. In MFCS, vol. 2747 of Lect. Notes Comput. Sci. Springer (2003) 662–670.
Verdú-Mas, J., Carrasco, R. and Calera–Rubio, J., Parsing with probabilistic strictly locally testable tree languages. IEEE Trans. Pattern Anal. Mach. Intell. 27 (2005) 1040–1050. Google ScholarPubMed
Wilke, T., An algebraic characterization of frontier testable tree languages. Theoret. Comput. Sci. 154 (1996) 85–106. Google Scholar