Greibach Normal Form for omega-Algebraic Systems and Weighted Simple omega-Pushdown Automata

Droste, Manfred; Dziadek, Sven; Kuich, Werner

doi:10.4230/lipics.fsttcs.2019.38

Cited by 1 publication

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“…A preliminary version of this paper appeared in [7]. In this version, we strengthen the first main result by proving that already ω-algebraic systems can be transformed into Greibach normal form.…”

Section: Introductionmentioning

confidence: 58%

“…In this version, we strengthen the first main result by proving that already ω-algebraic systems can be transformed into Greibach normal form. In [7], we only showed the existence of the Greibach normal form for mixed ω-algebraic systems. The stronger result in this work allows us to generalize the second main result: weighted simple ω-pushdown recognize all ω-algebraic series.…”

Section: Introductionmentioning

confidence: 94%

“…Lemma 9. The solution (7) is the first canonical solution of the mixed ω-algebraic system ( * ), ( * * ), ( * * * ).…”

Section: Greibach Normal Form For Mixed ω-Algebraic Systemsmentioning

confidence: 99%

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Greibach Normal Form for $ω$-Algebraic Systems and Weighted Simple $ω$-Pushdown Automata

Droste,

Dziadek,

Kuich

2020

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In weighted automata theory, many classical results on formal languages have been extended into a quantitative setting. Here, we investigate weighted context-free languages of infinite words, a generalization of ω-context-free languages (Cohen, Gold 1977) and an extension of weighted context-free languages of finite words (Chomsky, Schützenberger 1963). As in the theory of formal grammars, these weighted context-free languages, or ω-algebraic series, can be represented as solutions of mixed ω-algebraic systems of equations and by weighted ω-pushdown automata.In our first main result, we show that (mixed) ω-algebraic systems can be transformed into Greibach normal form. We use the Greibach normal form in our second main result to prove that simple ω-reset pushdown automata recognize all ω-algebraic series. Simple ω-reset automata do not use -transitions and can change the stack only by at most one symbol. These results generalize fundamental properties of context-free languages to weighted context-free languages.

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Section: Introductionmentioning

confidence: 58%

Section: Introductionmentioning

confidence: 94%