Capacitated automata and systems

Capacitated automata (CAs), introduced by Kupferman and Tamir at 2014, are a variant of finite-state automata in which each transition is associated with a (possibly infinite) capacity that bounds the number of times the transition may be traversed in a single run. We continue the study of the theoretical properties of CA and solve problems that were left open by Kupferman and Tamir. We show that union and intersection of CAs involve an exponential blow-up and that determinization and complementation involve a doubly-exponential blow-up. This blow-up is carried over 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 decision problems, there are also cases in which succinctness comes at no price. The study of CAs concerns the linear-time approach. We continue to study the branching-time approach, where the corresponding model is that of capacitated systems, and the interesting relation between systems is simulation. We study a game-theoretic approach to simulation of capacitated systems, and prove that deciding simulation between capacitated systems is PSPACE-complete. Thus, while in the linear-time approach the naive algorithm that removes capacities from the CA is optimal, in the branching-time approach we can do better than capacity removal.