Nominal deterministic omega automata

Nominal sets, presheaf categories, and named sets have successfully served as models of the state space of process calculi featuring resource generation. More recently, automata built in such categories have been studied as acceptors of languages of finite words over infinite alphabets. In this paper we investigate automata whose state spaces are nominal sets, and that accept infinite words. These automata are a generalisation of deterministic Muller automata to the setting of nominal sets. We prove decidability of complement, union, intersection, emptiness and equivalence. This is shown using finite representations of the (otherwise infinite-state) defined class of automata. The definition of such operations enables model checking of systems featuring infinite behaviours, and resource allocation, to be implemented using automata-theoretic methods, like in the classical case.