The paper gives an example of a tree language G that is recognised by an unambiguous parity automaton and is Σ 1 1 -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 Π 1 1 . Using set G as a building block we construct an unambiguous language that is topologically harder than any countable boolean combination of Σ 1 1 and Π 1 1 sets. In particular the language is harder than any set in difference hierarchy of analytic sets considered by O. Finkel and P. Simonnet in the context of nondeterministic automata.
Firstly, a result of Hummel REF shows that unambiguous languages are topologically harder than deterministic ones, see Figure 1 .
Unambiguous Tree Languages Are Topologically Harder Than Deterministic Ones
EPTCS 96, 2012, pp. 247-260
Mathematics Computer Science