A Nivat Theorem for Weighted Alternating Automata over Commutative Semirings

Gustav Grabolle
(Universität Leipzig, Germany)

In this paper, we give a Nivat-like characterization for weighted alternating automata over commutative semirings (WAFA). To this purpose we prove that weighted alternating can be characterized as the concatenation of weighted finite tree automata (WFTA) and a specific class of tree homomorphism. We show that the class of series recognized by weighted alternating automata is closed under inverses of homomorphisms, but not under homomorphisms. We give a logical characterization of weighted alternating automata, which uses weighted MSO logic for trees. Finally we investigate the strong connection between weighted alternating automata and polynomial automata. Using the corresponding result for polynomial automata, we are able to prove that the ZERONESS problem for weighted alternating automata with the rational numbers as weights is decidable.

In Pierre Ganty and Davide Bresolin: Proceedings 12th International Symposium on Games, Automata, Logics, and Formal Verification (GandALF 2021), Padua, Italy, 20-22 September 2021, Electronic Proceedings in Theoretical Computer Science 346, pp. 241–257.
Published: 17th September 2021.

ArXived at: http://dx.doi.org/10.4204/EPTCS.346.16 bibtex PDF
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