Efficient enumeration of weighted tree languages over the tropical semiring

2019 ◽  
Vol 104 ◽  
pp. 119-130 ◽  
Author(s):  
Johanna Björklund ◽  
Frank Drewes ◽  
Niklas Zechner
Keyword(s):  
Weighted Tree ◽  
Tropical Semiring ◽  
Tree Languages

Principal abstract families of weighted tree languages

2020 ◽  
pp. 104657
Author(s):  
Zoltán Fülöp ◽  
Heiko Vogler
Keyword(s):  
Weighted Tree ◽  
Tree Languages

Characterizations of recognizable weighted tree languages by logic and bimorphisms

2015 ◽  
Vol 22 (4) ◽  
pp. 1035-1046 ◽  
Author(s):  
Zoltán Fülöp ◽  
Heiko Vogler
Keyword(s):  
Weighted Tree ◽  
Tree Languages

Rational Weighted Tree Languages with Storage and the Kleene-Goldstine Theorem

2019 ◽  
pp. 138-150 ◽  
Author(s):  
Zoltán Fülöp ◽  
Heiko Vogler
Keyword(s):  
Weighted Tree ◽  
Tree Languages

scholarly journals Local Weighted Tree Languages

2015 ◽  
Vol 22 (2) ◽  
pp. 393-402
Author(s):  
Zoltán Fülöp
Keyword(s):  
Weighted Tree ◽  
Tree Languages

DECOMPOSITION OF WEIGHTED MULTIOPERATOR TREE AUTOMATA

2009 ◽  
Vol 20 (02) ◽  
pp. 221-245 ◽  
Author(s):  
TORSTEN STÜBER ◽  
HEIKO VOGLER ◽  
ZOLTÁN FÜLÖP
Keyword(s):  
Tree Automata ◽  
Commutative Monoid ◽  
Weighted Tree ◽  
Tree Language ◽  
Bottom Up ◽  
Tree Series ◽  
Finite State ◽  
Tree Languages ◽  
Tree Transformation

Weighted multioperator tree automata (for short: wmta) are finite-state bottom-up tree automata in which the transitions are weighted with an operation taken from some multioperator monoid. A wmta recognizes a tree series which is a mapping from the set of trees to some commutative monoid. We prove that every wmta recognizable tree series can be decomposed into a relabeling tree transformation, a recognizable tree language, and a tree series computed by a homomorphism wmta; vice versa, the composition of an arbitrary relabeling tree transformation, a recognizable tree language, and a tree series computed by a homomorphism wmta yields a wmta recognizable tree series. We use this characterization result for specific multioperator monoids and prove (1) a new decomposition of polynomial bottom-up tree series transducers over semirings and (2) a new characterization of tree series which are recognizable by weighted tree automata over semirings, in terms of projections of local tree languages.

The partial clone of linear tree languages

2017 ◽  
Vol 60 (3) ◽  
pp. 640-654
Author(s):  
N. Lekkoksung ◽  
K. Denecke
Keyword(s):  
Partial Clone ◽  
Tree Languages

Languages Accepted by Weighted Restarting Automata*

2021 ◽  
Vol 180 (1-2) ◽  
pp. 151-177
Author(s):  
Qichao Wang
Keyword(s):  
General Class ◽  
Formal Languages ◽  
Input Word ◽  
Additional Requirement ◽  
Tropical Semiring

Weighted restarting automata have been introduced to study quantitative aspects of computations of restarting automata. In earlier works we studied the classes of functions and relations that are computed by weighted restarting automata. Here we use them to define classes of formal languages by restricting the weight associated to a given input word through an additional requirement. In this way, weighted restarting automata can be used as language acceptors. First, we show that by using the notion of acceptance relative to the tropical semiring, we can avoid the use of auxiliary symbols. Furthermore, a certain type of word-weighted restarting automata turns out to be equivalent to non-forgetting restarting automata, and another class of languages accepted by word-weighted restarting automata is shown to be closed under the operation of intersection. This is the first result that shows that a class of languages defined in terms of a quite general class of restarting automata is closed under intersection. Finally, we prove that the restarting automata that are allowed to use auxiliary symbols in a rewrite step, and to keep on reading after performing a rewrite step can be simulated by regular-weighted restarting automata that cannot do this.

Tree Rewriting Systems, Combinatory Weak Reduction Systems and Type Free Languages1

1982 ◽  
Vol 5 (3-4) ◽  
pp. 279-299
Author(s):  
Alberto Pettorossi
Keyword(s):  
Combinatory Logic ◽  
Rewriting Systems ◽  
Tree Transducers ◽  
Tree Languages ◽  
One To One ◽  
The One ◽  
Weak Reduction

In this paper we consider combinators as tree transducers: this approach is based on the one-to-one correspondence between terms of Combinatory Logic and trees, and on the fact that combinators may be considered as transformers of terms. Since combinators are terms themselves, we will deal with trees as objects to be transformed and tree transformers as well. Methods for defining and studying tree rewriting systems inside Combinatory Weak Reduction Systems and Weak Combinatory Logic are also analyzed and particular attention is devoted to the problem of finiteness and infinity of the generated tree languages (here defined). This implies the study of the termination of the rewriting process (i.e. reduction) for combinators.

Weighted Tree Automata and Tree Transducers

2009 ◽  
pp. 313-403 ◽  
Author(s):  
Zoltán Fülöp ◽  
Heiko Vogler
Keyword(s):  
Tree Automata ◽  
Weighted Tree ◽  
Tree Transducers ◽  
Weighted Tree Automata
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