Unambiguisability and Register Minimisation of Min-Plus Models
For researchers in automata theory and formal verification, this work provides a decidability result for a fundamental problem and an undecidability result that sets limits on register minimisation.
The paper resolves the long-standing open problem of deciding unambiguisability for min-plus weighted automata (WFAs) by showing it is decidable via reduction to determinisability. It also proves that counter minimisation for tropical Cost Register Automata (CRAs) is undecidable, even for a fixed number of registers (7).
We study the unambiguisability problem for min-plus (tropical) weighted automata (WFAs), and the counter-minimisation problem for tropical Cost Register Automata (CRAs), which are expressively-equivalent to WFAs. Both problems ask whether the "amount of nondeterminism" in the model can be reduced. We show that WFA unambiguisability is decidable, thus resolving this long-standing open problem. Our proof is via reduction to WFA determinisability, which was recently shown to be decidable. On the negative side, we show that CRA counter minimisation is undecidable, even for a fixed number of registers (specifically, already for 7 registers).