|Publication ahead of print|
RAIRO-Theor. Inf. Appl.
|Published online||11 July 2018|
State hyperstructures of tree automata based on lattice-valued logic
Faculty of Mathematical Sciences, Shahrood University of Technology,
* Corresponding author: Ghorani@shahroodut.ac.ir
Accepted: 14 May 2018
In this paper, an association is organized between the theory of tree automata on one hand and the hyperstructures on the other hand, over complete residuated lattices. To this end, the concept of order of the states of a complete residuated lattice-valued tree automaton (simply ℒ-valued tree automaton) is introduced along with several equivalence relations in the set of the states of an ℒ-valued tree automaton. We obtain two main results from this study: one of the relations can lead to the creation of Kleene’s theorem for ℒ-valued tree automata, and the other one leads to the creation of a minimal ℒ-valued tree automaton that accepts the same language as the given one.
Mathematics Subject Classification: 68Q70 / 68Q45 / 20N25 / 20N20
Key words: Tree automaton / lattice-valued logic / Kleene’s theorem / hypergroup / minimization
© 2018, EDP Sciences
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