scholarly journals Weighted tree automata and weighted logics

2006 ◽  
Vol 366 (3) ◽  
pp. 228-247 ◽  
Author(s):  
Manfred Droste ◽  
Heiko Vogler
Keyword(s):  
Tree Automata ◽  
Weighted Tree ◽  
Weighted Tree Automata ◽  
Weighted Logics

scholarly journals Crisp-determinization of weighted tree automata over strong bimonoids

2021 ◽  
Vol vol. 23 no. 1 (Automata, Logic and Semantics) ◽  
Author(s):  
Zoltán Fülöp ◽  
Dávid Kószó ◽  
Heiko Vogler
Keyword(s):  
Finite Order ◽  
Positive Answer ◽  
Order Property ◽  
Sufficient Condition ◽  
Tree Automata ◽  
Weighted Tree ◽  
Bottom Up ◽  
Initial Algebra ◽  
Initial Algebra Semantics ◽  
Weighted Tree Automata

We consider weighted tree automata (wta) over strong bimonoids and their initial algebra semantics and their run semantics. There are wta for which these semantics are different; however, for bottom-up deterministic wta and for wta over semirings, the difference vanishes. A wta is crisp-deterministic if it is bottom-up deterministic and each transition is weighted by one of the unit elements of the strong bimonoid. We prove that the class of weighted tree languages recognized by crisp-deterministic wta is the same as the class of recognizable step mappings. Moreover, we investigate the following two crisp-determinization problems: for a given wta ${\cal A}$, (a) does there exist a crisp-deterministic wta which computes the initial algebra semantics of ${\cal A}$ and (b) does there exist a crisp-deterministic wta which computes the run semantics of ${\cal A}$? We show that the finiteness of the Nerode algebra ${\cal N}({\cal A})$ of ${\cal A}$ implies a positive answer for (a), and that the finite order property of ${\cal A}$ implies a positive answer for (b). We show a sufficient condition which guarantees the finiteness of ${\cal N}({\cal A})$ and a sufficient condition which guarantees the finite order property of ${\cal A}$. Also, we provide an algorithm for the construction of the crisp-deterministic wta according to (a) if ${\cal N}({\cal A})$ is finite, and similarly for (b) if ${\cal A}$ has finite order property. We prove that it is undecidable whether an arbitrary wta ${\cal A}$ is crisp-determinizable. We also prove that both, the finiteness of ${\cal N}({\cal A})$ and the finite order property of ${\cal A}$ are undecidable.

Ambiguity Hierarchies for Weighted Tree Automata

2021 ◽  
pp. 140-151
Author(s):  
Andreas Maletti ◽  
Teodora Nasz ◽  
Kevin Stier ◽  
Markus Ulbricht
Keyword(s):  
Tree Automata ◽  
Weighted Tree ◽  
Weighted Tree Automata

scholarly journals Minimizing deterministic weighted tree automata

2009 ◽  
Vol 207 (11) ◽  
pp. 1284-1299 ◽  
Author(s):  
Andreas Maletti
Keyword(s):  
Tree Automata ◽  
Weighted Tree ◽  
Weighted Tree Automata

scholarly journals A Kleene theorem for weighted tree automata over tree valuation monoids

2019 ◽  
Vol 269 ◽  
pp. 104445 ◽  
Author(s):  
Doreen Götze ◽  
Zoltán Fülöp ◽  
Manfred Droste
Keyword(s):  
Tree Automata ◽  
Weighted Tree ◽  
Weighted Tree Automata ◽  
Kleene Theorem
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