Probabilistic Finite Automaton Emptiness is undecidable
Formal Languages and Automata Theory
2024-06-07 v2
Abstract
It is undecidable whether the language recognized by a probabilistic finite automaton is empty. Several other undecidability results, in particular regarding problems about matrix products, are based on this important theorem. We present three proofs of this theorem from the literature in a self-contained way, and we derive some strengthenings. For example, we show that the problem remains undecidable for a fixed probabilistic finite automaton with 11 states, where only the starting distribution is given as input.
Cite
@article{arxiv.2405.03035,
title = {Probabilistic Finite Automaton Emptiness is undecidable},
author = {Günter Rote},
journal= {arXiv preprint arXiv:2405.03035},
year = {2024}
}
Comments
63 pages, 14 figures, 2 tables, 53 footnotes, 11 sections plus 1 appendix. Added another proof and more history, which had been overlooked before