Automata operating on infinite objects provide an invaluable tool for the
specification and verification of the ongoing behavior of infinite systems.
Coalgebra automata generalize the well-known automata that operate on
specific types of infinite structures such as words/streams, trees, graphs or
transition systems. The motivation underlying the introduction of coalgebra
automata is to gain a deeper understanding of this branch of automata theory
by studying properties of automata in a uniform manner, parametric in the type
of the recognized structures. Coalgebraic automata theory thus contributes to
Universal Coalgebra as a mathematical theory of state-based evolving systems.

In the talk we introduce parity automata that correspond to coalgebraic modal
fixpoint logic based on predicate liftings. More specifically, we define the
notion of a $\Lambda$-automaton, where $\Lambda$ is a set of predicate liftings for
a given functor $T$, and the notion of acceptance for such an automaton, which
is defined in terms of a parity acceptance game. The main result that we discuss
states that  a $\Lambda$-automaton accepts a pointed coalgebra iff it accepts a
finite coalgebra which is obtained from the automaton itself by some effective
construction. This result corresponds to a general bounded model property for
coalgebraic modal fixpoint logics. Time permitting we discuss some complexity
issues, and relate our results to work by Cirstea, Kupke and Pattinson.