Günter Rote:

Probabilistic Finite Automaton Emptiness is undecidable

Manuscript, June 2024, 63 pages, arXiv:2405.03035 [cs.FL]  →BibTeX

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.

  pdf file
other papers about this subject
Last update: June 6, 2024.