Undecidable Problems for Probabilistic Automata of Fixed Dimension

摘要

We prove that several problems associated with probabilistic finite automata are undecidable for automata whose number of input letters and number of states are fixed. As a corollary of one of our results we prove that the problem of determining if the set of all products of two 47 x 47 matrices with nonnegative rational entries is bounded is undecidable.