From Tree Automata to Rational Tree Expressions

2018 ◽  
Vol 29 (06) ◽  
pp. 1045-1062
Author(s):  
Younes Guellouma ◽  
Hadda Cherroun
Keyword(s):  
Unique Solution ◽  
Equation System ◽  
Tree Automaton ◽  
Tree Automata ◽  
Finite Tree ◽  
Rational Expression ◽  
Tree Expression

We propose a construction of rational tree expression from finite tree automata. First, we define rational expression equation systems and we propose a substitution based method to find the unique solution. Furthermore, we discuss the case of recursion being present in an equation system, and then show under which restrictions such systems can effectively be solved. Secondly, we show that any finite tree automaton can be associated to a rational tree equation system, and that the latter can in turn be resolved. Finally, using the previous steps, a rational tree expression equivalent to the underlying automaton is extracted.

The Bottom-Up Position Tree Automaton and the Father Automaton

2020 ◽  
pp. 1-18
Author(s):  
Samira Attou ◽  
Ludovic Mignot ◽  
Djelloul Ziadi
Keyword(s):  
Tree Automaton ◽  
Tree Automata ◽  
Top Down ◽  
Bottom Up ◽  
Regular Tree ◽  
The One ◽  
Tree Expression

The conversion of a given regular tree expression into a tree automaton has been widely studied. However, classical interpretations are based upon a top-down interpretation of tree automata. In this paper, we propose new constructions based on Gluskov’s one and on the one by Ilie and Yu using a bottom-up interpretation. One of the main goals of this technique is to consider as a next step the links with deterministic recognizers, something which cannot be done with classical top-down approaches.

Deciding Equivalence of Finite Tree Automata

1990 ◽  
Vol 19 (3) ◽  
pp. 424-437 ◽  
Author(s):  
Helmut Seidl
Keyword(s):  
Tree Automata ◽  
Finite Tree

HYPER-MINIMIZATION FOR DETERMINISTIC TREE AUTOMATA

2013 ◽  
Vol 24 (06) ◽  
pp. 815-830 ◽  
Author(s):  
ARTUR JEŻ ◽  
ANDREAS MALETTI
Keyword(s):  
Finite Difference ◽  
Minimization Problem ◽  
Fast Algorithms ◽  
Input Tree ◽  
Tree Automaton ◽  
Tree Automata ◽  
Compression Technique ◽  
Bottom Up ◽  
Finite State ◽  
Transition Table

Hyper-minimization is a recent automaton compression technique that can reduce the size of an automaton beyond the limits imposed by classical minimization. The additional compression power is enabled by allowing a finite difference in the represented language. The necessary theory for hyper-minimization is developed for (bottom-up) deterministic tree automata. The hyper-minimization problem for deterministic tree automata is reduced to the hyper-minimization problem for deterministic finite-state string automata, for which fast algorithms exist. The fastest algorithm obtained in this way runs in time [Formula: see text], where m is the size of the transition table and n is the number of states of the input tree automaton.

scholarly journals A Congruence-Based Perspective on Finite Tree Automata

2022 ◽  
Vol 184 (1) ◽  
pp. 1-47
Author(s):  
Pierre Ganty ◽  
Elena Gutiérrez ◽  
Pedro Valero
Keyword(s):  
Expressive Power ◽  
Tree Automata ◽  
Minimization Algorithm ◽  
Top Down ◽  
Finite Tree ◽  
Bottom Up ◽  
Original Result

We provide new insights on the determinization and minimization of tree automata using congruences on trees. From this perspective, we study a Brzozowski’s style minimization algorithm for tree automata. First, we prove correct this method relying on the following fact: when the automata-based and the language-based congruences coincide, determinizing the automaton yields the minimal one. Such automata-based congruences, in the case of word automata, are defined using pre and post operators. Now we extend these operators to tree automata, a task that is particularly challenging due to the reduced expressive power of deterministic top-down (or equivalently co-deterministic bottom-up) automata. We leverage further our framework to offer an extension of the original result by Brzozowski for word automata.

State hyperstructures of tree automata based on lattice-valued logic

2018 ◽  
Vol 52 (1) ◽  
pp. 23-42 ◽  
Author(s):  
Maryam Ghorani
Keyword(s):  
Residuated Lattice ◽  
Residuated Lattices ◽  
The Other ◽  
Equivalence Relations ◽  
Tree Automaton ◽  
Tree Automata ◽  
Other Hand ◽  
Complete Residuated Lattice ◽  
The Creation ◽  
The Given

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 v-valued tree automaton that accepts the same language as the given one.

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