Unambiguous Buchi is weak
Henryk Michalewski, Micha{\l} Skrzypczak

TL;DR
This paper proves a complexity collapse for unambiguous nondeterministic parity tree automata, showing their recognized languages are simpler than previously thought, especially for unambiguous Büchi automata which recognize Borel languages.
Contribution
It establishes a new complexity collapse result for unambiguous automata, linking unambiguity with lower descriptive complexity in tree automata.
Findings
Unambiguous automata with certain parity conditions recognize languages in lower complexity classes.
Unambiguous Büchi automata recognize Borel languages.
First known result linking unambiguity to parity index collapse.
Abstract
A non-deterministic automaton running on infinite trees is unambiguous if it has at most one accepting run on every tree. The class of languages recognisable by unambiguous tree automata is still not well-understood. In particular, decidability of the problem whether a given language is recognisable by some unambiguous automaton is open. Moreover, there are no known upper bounds on the descriptive complexity of unambiguous languages among all regular tree languages. In this paper we show the following complexity collapse: if a non-deterministic parity tree automaton is unambiguous and its priorities are between and then the language recognised by is in the class . A particular case of this theorem is for : if is an unambiguous Buchi tree automaton then is recognisable by a weak alternating automaton (or equivalently definable in weak…
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Taxonomy
Topicssemigroups and automata theory · Computability, Logic, AI Algorithms · Advanced Algebra and Logic
