Polynomially Ambiguous Probabilistic Automata on Restricted Languages
Abstract
We consider the computability and complexity of decision questions for Probabilistic Finite Automata (PFA) with sub-exponential ambiguity. We show that the emptiness problem for strict and non-strict cut-points of polynomially ambiguous commutative PFA remains undecidable, implying that the problem is undecidable when inputs are from a letter monotonic language. We show that the problem remains undecidable over a binary input alphabet when the input word is over a bounded language, in the noncommutative case. In doing so, we introduce a new technique based upon the Turakainen construction of a PFA from a Weighted Finite Automata which can be used to generate PFA of lower dimensions and of subexponential ambiguity. We also study freeness/injectivity problems for polynomially ambiguous PFA and study the border of decidability and tractability for various cases.
Keywords
Cite
@article{arxiv.1902.09407,
title = {Polynomially Ambiguous Probabilistic Automata on Restricted Languages},
author = {Paul C. Bell},
journal= {arXiv preprint arXiv:1902.09407},
year = {2020}
}
Comments
Amended an issue regarding commutativity of matrices in Theorem 1 to show why the matrices commute