Handbook of theoretical computer science (vol. B)
An introduction to symbolic dynamics and coding
An introduction to symbolic dynamics and coding
Symbolic dynamics and finite automata
Handbook of formal languages, vol. 2
Languages, automata, and logic
Handbook of formal languages, vol. 3
Complexity of weak acceptance conditions in tree automata
Information Processing Letters
On the Finite Degree of Ambiguity of Finite Tree Automata
FCT '89 Proceedings of the International Conference on Fundamentals of Computation Theory
Parsing with Probabilistic Strictly Locally Testable Tree Languages
IEEE Transactions on Pattern Analysis and Machine Intelligence
A hierarchy of shift equivalent sofic shifts
Theoretical Computer Science - Mathematical foundations of computer science 2004
Decidability of Conjugacy of Tree-Shifts of Finite Type
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Elements of Automata Theory
Sofic and almost of finite type tree-shifts
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
Sofic systems and encoding data
IEEE Transactions on Information Theory
Minimal presentations for irreducible sofic shifts
IEEE Transactions on Information Theory
Theoretical Computer Science
Cellular automata on regular rooted trees
CIAA'12 Proceedings of the 17th international conference on Implementation and Application of Automata
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We introduce the notion of sofic tree-shifts which corresponds to symbolic dynamical systems of infinite ranked trees accepted by finite tree automata. We show that, contrary to shifts of infinite sequences, there is no unique reduced deterministic irreducible tree automaton accepting an irreducible sofic tree-shift, but that there is a unique synchronized one, called the Fischer automaton of the tree-shift. We define the notion of almost of finite type tree-shift which are sofic tree-shifts accepted by a tree automaton which is both deterministic and co-deterministic with a finite delay. It is a meaningful intermediate dynamical class in between irreducible finite type tree-shifts and irreducible sofic tree-shifts. We characterize the Fischer automaton of an almost of finite type tree-shift and we design an algorithm to check whether a sofic tree-shift is almost of finite type. We prove that the Fischer automaton is a topological conjugacy invariant of the underlying irreducible sofic tree-shift.