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Frederic Dörband

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I&C Journal 2024 Journal Article

Rational weighted tree languages with storage

Frederic Dörband
Zoltán Fülöp
Heiko Vogler

We define the class of rational weighted tree languages with storage over complete, not necessarily commutative, semirings and we repeat its characterization by weighted regular tree grammars with storage. Moreover, we show an alternative proof of the fact that the class of rational weighted tree languages with storage is closed under the rational operations, i. e. , top-concatenation, scalar multiplication, sum, tree concatenation, and Kleene-star, where the latter two closure results require that the storage has a reset instruction.

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I&C Journal 2021 Journal Article

Kleene and Büchi theorems for weighted forest languages over M-monoids

Frederic Dörband

We consider forests as tuples of trees and introduce weighted forest automata (wfa) over M-monoids. A wfa acts on each individual tree in a forest like a weighted tree automaton over the same M-monoid. In order to combine the values of trees in forests, a wfa uses an associative multiplication operation that distributes over the addition of the M-monoid. We continue by introducing two semantics for wfa, an “initial algebra”-like semantic and a run-semantic, and prove that these semantics are equal for distributive M-monoids. We prove that our automaton model accepts finite products of recognizable weighted tree languages over M-monoids. Next, we introduce rational weighted forest expressions and forest M-expressions over M-monoids and show that the classes of languages generated by these formalisms coincide with recognizable weighted forest languages under certain conditions on the underlying M-monoid.

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