Crisp-Determinization of Weighted Tree Automata over Additively Locally Finite and Past-Finite Monotonic Strong Bimonoids Is Decidable

Droste, Manfred; Fülöp, Zoltán; Kószó, Dávid; Vogler, Heiko

doi:10.1007/978-3-030-62536-8_4

Cited by 4 publications

(3 citation statements)

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“…If we allow a crisp-deterministic weighted automaton to have an infinite set of states, as we do in this paper, then any weighted finite automaton can be converted into an equivalent crisp-deterministic weighted automaton, and the basic problem is to perform such a conversion that will provide an equivalent crisp-deterministic weighted automaton with a finite number of states, as small as possible. For information on crisp-determinization of weighted tree automata we refer to [14,15].…”

Section: Introductionmentioning

confidence: 99%

Weighted Automata over Vector Spaces

Damljanović,

Ćirić,

Ignjatović

2023

Electron. Proc. Theor. Comput. Sci.

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Section: Introductionmentioning

confidence: 99%

Weighted Automata over Vector Spaces

Damljanović,

Ćirić,

Ignjatović

2023

Electron. Proc. Theor. Comput. Sci.

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“…In a similar way, finite-state tree automata have been extended to weighted tree automata (wta) over various weight algebras, e.g., complete distributive lattices [IF75,ÉL07], fields [BR82], commutative semirings [AB87], strong bimonoids [Rad10,DFKV20], multioperator monoids [Kui99, FMV09, FSV12], and tree-valuation monoids [DHV15]. In any case, a wta A recognizes a weighted tree language [[A]] (or: formal tree series), i.e., a mapping from the set of input trees to the carrier set of the weight algebra.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we investigate the two mentioned questions for wta over pastfinite monotonic strong bimonoids. It is an extended version of [DFKV20] and our main results are the following:…”

Section: Introductionmentioning

confidence: 99%

Finite-image property of weighted tree automata over past-finite monotonic strong bimonoids

Droste¹,

Fülöp²,

Kószó³

et al. 2021

Preprint

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We consider weighted tree automata over strong bimonoids (for short: wta). A wta A has the finite-image property if its recognized weighted tree language [[A]] has finite image; moreover, A has the preimage property if the preimage under [[A]] of each element of the underlying strong bimonoid is a recognizable tree language. For each wta A over a past-finite monotonic strong bimonoid we prove the following results. In terms of A's structural properties, we characterize whether it has the finite-image property. We characterize those past-finite monotonic strong bimonoids such that for each wta A it is decidable whether A has the finite-image property. In particular, the finite-image property is decidable for wta over past-finite monotonic semirings. Moreover, we prove that A has the preimage property. All our results also hold for weighted string automata.

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