On the capacity of capacitated automata

Capacitated automata (CAs) have been recently introduced in [8] as a variant of finite-state automata in which each transition is associated with a (possibly infinite) capacity. The capacity bounds the number of times the transition may be traversed in a single run. The study in [8] includes preliminary results about the expressive power of CAs, their succinctness, and the complexity of basic decision problems for them. We continue the investigation of the theoretical properties of CAs and solve problems that have been left open in [8]. In particular, we show that union and intersection of CAs involve an exponential blow-up and that their determinization involves a doubly-exponential blow up. This blow-up is carried over to complementation and to the complexity of the universality and containment problems, which we show to be EXPSPACE-complete. On the positive side, capacities do not increase the complexity when used in the deterministic setting. Also, the containment problem for nondeterministic CAs is PSPACE-complete when capacities are used only in the left-hand side automaton. Our results suggest that while the succinctness of CAs leads to a corresponding increase in the complexity of some of their decision problems, there are also settings in which succinctness comes at no price.