2024/05/05 by Günter Rote, Rote, Günter
Computer Science · #Computability, Logic, AI Algorithms #F.1.1 #F.4.3 #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL) #Machine Learning and Algorithms #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2405.03035
openalex publication_date 2024/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.