The paper gives an example of a tree language G that is recognised by an unambiguous parity automaton and is Σ1-complete (analytic-complete) as a set in Cantor space. This already shows that the unambiguous languages are topologically more complex than the deterministic ones, that are all in Π1. Using set G as a building block we construct an unambiguous language that is topologically harder th...

We introduce a machine model for the execution of strategies in (regular) infinite games that refines the standard model of Mealy automata. This model of controllers is formalized in the terminological framework of Turing machines. We show how polynomially sized controllers can be found for Muller and Streett games. We are able to distinguish aspects of executing strategies (”size”, ”latency”, ...

In this paper, ω-closed sets and ω-open sets are used to define and investigate a new class of functions. Relationships between this new class and other classes of functions are established.