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arXiv · 2610.08525

Stronger bounds on the degree of ambiguity of finite automata

Stefan Kiefer·Filip Mazowiecki·Andrew Ryzhikov·Antoni Wiśniewski
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Abstract

Ambiguity measures the number of accepting runs in nondeterministic finite automata (NFA). We consider finitely ambiguous NFA, where there exists a constant $N$ such that over every word $w$ there are at most $N$ accepting runs. In such a case we also say that the NFA is $N$-ambiguous. Importantly $N$ depends only on the NFA, it does not depend on the length of the word. Weber and Seidl showed that every NFA is $N$-ambiguous for $N = 2^{O(n \log n)}$, where $n$ is the number of states. We improve this to $N = 2^{O(n)}$, which is asymptotically tight.

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Stefan Kiefer, Filip Mazowiecki, Andrew Ryzhikov, Antoni Wiśniewski. 2026-10-06. Stronger bounds on the degree of ambiguity of finite automata. https://arxiv.org/abs/2610.08525

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