On finitely ambiguous Büchi automata

Unambiguous B\"uchi automata, i.e. B\"uchi automata allowing only one accepting run per word, are a useful restriction of B\"uchi automata that is well-suited for probabilistic model-checking. In this paper we propose a more permissive variant, namely finitely ambiguous B\"uchi automata, a generalisation where each word has at most \(k\) accepting runs, for some fixed \(k\). We adapt existing notions and results concerning finite and bounded ambiguity of finite automata to the setting of \(\omega\)-languages and present a translation from arbitrary nondeterministic B\"uchi automata with \(n\) states to finitely ambiguous automata with at most \(3^n\) states and at most \(n\) accepting runs per word.