Minimizing Deterministic 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.

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Kleene’s Theorem for Weighted Tree-Automata

Fundamentals of Computation Theory - Lecture Notes in Computer Science ◽

10.1007/978-3-540-45077-1_36 ◽

2003 ◽

pp. 387-399 ◽

Cited By ~ 4

Author(s):

Christian Pech

Keyword(s):

Tree Automata ◽

Weighted Tree ◽

Weighted Tree Automata

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Ambiguity Hierarchies for Weighted Tree Automata

Implementation and Application of Automata - Lecture Notes in Computer Science ◽

10.1007/978-3-030-79121-6_12 ◽

2021 ◽

pp. 140-151

Author(s):

Andreas Maletti ◽

Teodora Nasz ◽

Kevin Stier ◽

Markus Ulbricht

Keyword(s):

Tree Automata ◽

Weighted Tree ◽

Weighted Tree Automata

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Approximate minimization of weighted tree automata

Information and Computation ◽

10.1016/j.ic.2020.104654 ◽

2020 ◽

pp. 104654

Author(s):

Borja Balle ◽

Guillaume Rabusseau

Keyword(s):

Tree Automata ◽

Weighted Tree ◽

Weighted Tree Automata ◽

Approximate Minimization

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