We study capacitated automata (CAs) [10], where transitions correspond to resources and have capacities, bounding the number of times they may be traversed. We follow the utilization semantics of CAs and view them as recognizers of multi-languages - sets of multisets of words, where a multiset S of words is in the multi-language of a CA A if all the words in S can be mutually accepted by A: the multiset of runs on all the words in S together respects the bounds induced by the capacities. Thus, capacitated automata model possible utilizations of systems with bounded resources. We study the basic properties of CAs: their expressive power in the nondeterministic and deterministic models, closure under classical operations, and the complexity of basic decision problems.
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