An improved translation from alternating parity automata on infinite words to alternating
weak automata is given. The blow-up of the number of states is related to the size of the …

Different types of automata over words and trees offer different trade-offs between
expressivity, conciseness, and the complexity of decision procedures. Alternating weak …

We prove that ω2 strictly bounds the iterations required for modal definable functions to
reach a fixed point across all countable structures. The result corrects and extends the …

We focus on formulae $\exists X.\,\varphi (\vec {Y}, X) $ of monadic second-order logic over
the full binary tree, such that the witness $ X $ is a well-founded set. The ordinal rank …

The parity index problem of tree automata asks, given a regular tree language L, what is the
least number of priorities of a nondeterministic parity tree automaton that recognises L. This …

We show that it is decidable whether two regular languages of infinite trees are separable by
a deterministic language, resp., a game language. We consider two variants of separability …

$$\varSigma ^{\mu }_2$$ is decidable for $$\varPi ^{\mu }_2$$ | SpringerLink Skip to main
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We show an algorithm that for a given regular tree language L decides if L is in Pi^ 0_2, that
is if L belongs to the second level of Borel Hierarchy. Moreover, if L is in Pi^ 0_2, then we …

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 …

This work is a study of the class of non-deterministic automata on infinite trees that are
unambiguous ie have at most one accepting run on every tree. The motivating question asks …