4 research outputs found
Weak index versus Borel rank
We investigate weak recognizability of deterministic languages of infinite
trees. We prove that for deterministic languages the Borel hierarchy and the
weak index hierarchy coincide. Furthermore, we propose a procedure computing
for a deterministic automaton an equivalent minimal index weak automaton with a
quadratic number of states. The algorithm works within the time of solving the
emptiness problem
Regular tree languages in low levels of the Wadge Hierarchy
In this article we provide effective characterisations of regular languages
of infinite trees that belong to the low levels of the Wadge hierarchy. More
precisely we prove decidability for each of the finite levels of the hierarchy;
for the class of the Boolean combinations of open sets (i.e.
the union of the first levels); and for the Borel class
(i.e. for the union of the first levels)
On the topological complexity of weakly recognizable tree languages
Abstract. We show that the family of tree languages recognized by weak alternating automata is closed by three set theoretic operations that correspond to sum, multiplication by ordinals <ω ω, and pseudoexponentiation with the base ω1 of the Wadge degrees. In consequence, the Wadge hierarchy of weakly recognizable tree languages has the height of at least ε0, that is the least fixed point of the exponentiation with the base ω.