151. Decidability Boundaries for the Finite-Image Property of Weighted Finite Automata.
- Author
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Droste, Manfred, Fülöp, Zoltán, and Kószó, Dávid
- Subjects
- *
FINITE state machines , *ROBOTS - Abstract
A weighted finite automaton has the finite-image property if the image of the weighted language associated with it is finite. We show two undecidability results concerning the finite-image property of weighted finite automata over semirings, respectively strong bimonoids. Firstly, we give a computable idempotent commutative past-finite ordered semiring such that it is undecidable, for an arbitrary deterministic weighted finite automaton over that semiring, whether has the finite-image property. Secondly, we give a computable commutative past-finite monotonic ordered strong bimonoid such that it is undecidable, for an arbitrary weighted finite automaton over that strong bimonoid, whether has the finite-image property. This shows that recent decidability results for suitable weighted finite automata over past-finite monotonic strong bimonoids cannot be extended to natural classes of ordered semirings and ordered strong bimonoids without further assumptions. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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