Is the following problem decidable: Given \(A\), a weighted automaton (WA) over the \((\min,+)\) semiring, answer whether \(A\) has an equivalent deterministic WA?

*Remarks:* The problem is equivalent when considering only automata with
weights in \(\{0,1\}\) (a.k.a. distance automata). The problem is known to be
decidable for polynomially-ambiguous WA. For the general case of
exponentially-ambiguous WA, we don't even have any interesting examples where
determinization incurs a significant state explosion.