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.
Distance desert automata and the star height problem
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Unambiguisability and Register Minimisation of Min-Plus Models
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.