On Finite and Polynomial Ambiguity of Weighted Tree Automata

Paul, Erik

doi:10.1007/978-3-662-53132-7_30

Cited by 6 publications

(3 citation statements)

References 21 publications

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“…, A N and then analyze the interplay of these latter automata. We can do so as in fact, every finitely ambiguous WTA can be decomposed into finitely many unambiguous WTA [10,40]. This is a common approach when dealing with finite ambiguity [10,41,42] and is also used by Bala in the corresponding proof for words [26].…”

Section: The Criterion For Finite Sequentialitymentioning

confidence: 99%

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Finite Sequentiality of Finitely Ambiguous Max-Plus Tree Automata

Paul

2021

Theory Comput Syst

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We 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.

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Section: The Criterion For Finite Sequentialitymentioning

confidence: 99%

“…Lemma 1 [40] Let A be a finitely ambiguous WTA over a semiring K and a ranked alphabet Γ , then we can effectively find an integer M ∈ N and construct finitely many unambiguous WTA A 1 , . .…”

Section: The Criterion For Finite Sequentialitymentioning

confidence: 99%

Finite Sequentiality of Finitely Ambiguous Max-Plus Tree Automata

Paul

2021

Theory Comput Syst

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“…In [26], polynomially ambiguous, finitely ambiguous and unambiguous weighted automata (without assuming aperiodicity) over commutative semirings were shown to be expressively equivalent to suitable fragments of weighted monadic second order logic. This was further extended in [32] to cover polynomial degrees and weighted tree automata.…”

Section: Related Workmentioning

confidence: 99%

Aperiodic Weighted Automata and Weighted First-Order Logic

Droste¹,

Gastin²

2019

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By fundamental results of Schützenberger, McNaughton and Papert from the 1970s, the classes of first-order definable and aperiodic languages coincide. Here, we extend this equivalence to a quantitative setting. For this, weighted automata form a general and widely studied model. We define a suitable notion of a weighted first-order logic. Then we show that this weighted first-order logic and aperiodic polynomially ambiguous weighted automata have the same expressive power. Moreover, we obtain such equivalence results for suitable weighted sublogics and finitely ambiguous or unambiguous aperiodic weighted automata. Our results hold for general weight structures, including all semirings, average computations of costs, bounded lattices, and others.

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