scholarly journals Finite Sequentiality of Unambiguous Max-Plus Tree Automata

2021 ◽  
Author(s):  
Erik Paul
Keyword(s):  
Tree Automaton ◽  
Tree Automata ◽  
Plus Tree ◽  
The Given ◽  
Pointwise Maximum

AbstractWe show the decidability of the finite sequentiality problem for unambiguous max-plus tree automata. A max-plus tree automaton is called unambiguous if there is at most one accepting run on every tree. The finite sequentiality problem asks whether for a given max-plus tree automaton, there exist finitely many deterministic max-plus tree automata whose pointwise maximum is equivalent to the given automaton.

scholarly journals Finite Sequentiality of Finitely Ambiguous Max-Plus Tree Automata

2021 ◽  
Author(s):  
Erik Paul
Keyword(s):  
Tree Automaton ◽  
Tree Automata ◽  
Weighted Tree ◽  
Plus Tree ◽  
The Given ◽  
Pointwise Maximum

AbstractWe show that the finite sequentiality problem is decidable for finitely ambiguous max-plus tree automata. A max-plus tree automaton is a weighted tree automaton over the max-plus semiring. A max-plus tree automaton is called finitely ambiguous if the number of accepting runs on every tree is bounded by a global constant. The finite sequentiality problem asks whether for a given max-plus tree automaton, there exist finitely many deterministic max-plus tree automata whose pointwise maximum is equivalent to the given automaton.

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.

A minimization algorithm for fuzzy top-down tree automata over lattices

2020 ◽  
pp. 1-10
Author(s):  
M. Ghorani ◽  
S. Garhwal
Keyword(s):  
Minimization Problem ◽  
Time Complexity ◽  
Tree Automaton ◽  
Tree Automata ◽  
Minimization Algorithm ◽  
Top Down ◽  
Minimal Form ◽  
Minimization Algorithms ◽  
The Given

In this paper, we study fuzzy top-down tree automata over lattices ( LTA s , for short). The purpose of this contribution is to investigate the minimization problem for LTA s . We first define the concept of statewise equivalence between two LTA s . Thereafter, we show the existence of the statewise minimal form for an LTA . To this end, we find a statewise irreducible LTA which is equivalent to a given LTA . Then, we provide an algorithm to find the statewise minimal LTA and by a theorem, we show that the output statewise minimal LTA is statewise equivalent to the given input. Moreover, we compute the time complexity of the given algorithm. The proposed algorithm can be applied to any given LTA and, unlike some minimization algorithms given in the literature, the input doesn’t need to be a complete, deterministic, or reduced lattice-valued tree automaton. Finally, we provide some examples to show the efficiency of the presented algorithm.

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 From generic partition refinement to weighted tree automata minimization

2021 ◽  
Author(s):  
Thorsten Wißmann ◽  
Hans-Peter Deifel ◽  
Stefan Milius ◽  
Lutz Schröder
Keyword(s):  
Tree Automata ◽  
Weighted Tree ◽  
Transition Systems ◽  
Run Time Analysis ◽  
Deterministic Automata ◽  
Weighted Tree Automata ◽  
Run Time ◽  
The Given ◽  
Refinement Algorithm ◽  
Partition Refinement

AbstractPartition refinement is a method for minimizing automata and transition systems of various types. Recently, we have developed a partition refinement algorithm that is generic in the transition type of the given system and matches the run time of the best known algorithms for many concrete types of systems, e.g. deterministic automata as well as ordinary, weighted, and probabilistic (labelled) transition systems. Genericity is achieved by modelling transition types as functors on sets, and systems as coalgebras. In the present work, we refine the run time analysis of our algorithm to cover additional instances, notably weighted automata and, more generally, weighted tree automata. For weights in a cancellative monoid we match, and for non-cancellative monoids such as (the additive monoid of) the tropical semiring even substantially improve, the asymptotic run time of the best known algorithms. We have implemented our algorithm in a generic tool that is easily instantiated to concrete system types by implementing a simple refinement interface. Moreover, the algorithm and the tool are modular, and partition refiners for new types of systems are obtained easily by composing pre-implemented basic functors. Experiments show that even for complex system types, the tool is able to handle systems with millions of transitions.

A Practical Algorithm for the Uniform Membership Problem of Labeled Multidigraphs of Tree-Width 2 for Spanning Tree Automata

2017 ◽  
Vol 28 (05) ◽  
pp. 563-581 ◽  
Author(s):  
Akio Fujiyoshi
Keyword(s):  
Spanning Tree ◽  
Linear Time ◽  
Time Algorithm ◽  
Finite State Automaton ◽  
Linear Time Algorithm ◽  
Membership Problem ◽  
Tree Automaton ◽  
Tree Automata ◽  
Tree Width ◽  
Practical Algorithm

This paper presents a practical algorithm for the uniform membership problem of labeled multidigraphs of tree-width at most 2 for spanning tree automata. Though the theoretical existence of a linear-time algorithm for the membership problem for graphs of bounded tree-width was shown in the previous study, the implementation of the linear-time algorithm is expected to be impractical because it requires the construction of a finite-state automaton whose size is super-exponential in the size of the tree automaton and the tree-width of graphs. In addition, the tree automaton itself should be a part of the input in practical situations.

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.

SIMULATION OF SYSTOLIC TREE AUTOMATA ON TRELLIS AUTOMATA

1990 ◽  
Vol 01 (02) ◽  
pp. 87-110 ◽  
Author(s):  
EMANUELA FACHINI ◽  
JOZEF GRUSKA ◽  
ANDREA MAGGIOLO SCHETTINI ◽  
DAVIDE SANGIORGI
Keyword(s):  
Tree Automaton ◽  
Tree Automata ◽  
The Family

The relation between two basic types of systolic automata—tree automata and trellis automata—is investigated. First it is shown that for every natural t>1 there is a simple nonhomogeneous (actually regular and also modular) trellis [Formula: see text] such that any t-ary systolic tree automaton can be simulated in a universal and quite straighforward way on a trellis automaton over [Formula: see text]. This implies that the family of languages accepted by systolic tree automata, which is incomparable with the family of languages accepted by homogeneous systolic trellis automata, is actually contained in the family of languages accepted by trellis automata that are both regular and modular.

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.

RELATING TREE SERIES TRANSDUCERS AND WEIGHTED TREE AUTOMATA

2005 ◽  
Vol 16 (04) ◽  
pp. 723-741 ◽  
Author(s):  
ANDREAS MALETTI
Keyword(s):  
Tree Automata ◽  
Formal Representation ◽  
Weighted Tree ◽  
Bottom Up ◽  
Operation Symbol ◽  
Tree Series ◽  
Pumping Lemma ◽  
Emptiness Problem ◽  
Weighted Tree Automata ◽  
The Given

Bottom-up tree series transducers (tst) over the semiring [Formula: see text] are implemented with the help of bottom-up weighted tree automata (wta) over an extension of [Formula: see text]. Therefore bottom-up [Formula: see text]-weighted tree automata ([Formula: see text]-wta) with [Formula: see text] a distributive Ω-algebra are introduced. A [Formula: see text]-wta is essentially a wta but uses as transition weight an operation symbol of the Ω-algebra [Formula: see text] instead of a semiring element. The given tst is implemented with the help of a [Formula: see text]-wta, essentially showing that [Formula: see text]-wta are a joint generalization of tst (using IO-substitution) and wta. Then a semiring and a wta are constructed such that the wta computes a formal representation of the semantics of the [Formula: see text]-wta. The applicability of the obtained presentation result is demonstrated by deriving a pumping lemma for deterministic finite [Formula: see text]-wta from a known pumping lemma for deterministic finite wta. Finally, it is observed that the known decidability results for emptiness cannot be applied to obtain decidability of emptiness for finite [Formula: see text]-wta. Thus with help of a weaker version of the derived pumping lemma, decidability of the emptiness problem for finite [Formula: see text]-wta is shown under mild conditions on [Formula: see text].

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