Unambiguisability for min-plus weighted automata is decidable via reduction to determinisability, while counter minimization for tropical cost register automata is undecidable for seven or more registers.
What's decidable about weighted automata? Information and Computation , 282:104651
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Unary weighted automata over the tropical semiring admit a polynomial-time computable quadratic-size union representation of deterministic automata, implying coNP-completeness of determinisation and register minimisation.
New randomized reductions and faster algorithms for XNFA decision problems under polynomial or bounded ambiguity, extending to other semirings.
Weighted NetKAT extends NetKAT with semiring weights and weighted NetKAT automata to enable automatic verification of quantitative safety and reachability properties.
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