When is containment decidable for probabilistic automata
Laure Daviaud, Marcin Jurdziński, Ranko Lazić, Filip Mazowiecki, Guillermo A. Pérez, James Worrell · Warwick Research Archive Portal (University of Warwick) · 2018
The containment problem for quantitative automata is the natural quantitative generalisation of the classical language inclusion problem for Boolean automata. We study it for probabilistic automata, where it is known to be undecidable in general. We restrict our study to the class of probabilistic automata with bounded ambiguity. There, we show decidability (subject to Schanuel's conjecture) when one of the automata is assumed to be unambiguous while the other one is allowed to be finitely ambiguous. Furthermore, we show that this is close to the most general decidable fragment of this problem by proving that it is already undecidable if one of the automata is allowed to be linearly ambiguous.