English

What is known about the Value 1 Problem for Probabilistic Automata?

Formal Languages and Automata Theory 2014-10-15 v1

Abstract

The value 1 problem is a decision problem for probabilistic automata over finite words: are there words accepted by the automaton with arbitrarily high probability? Although undecidable, this problem attracted a lot of attention over the last few years. The aim of this paper is to review and relate the results pertaining to the value 1 problem. In particular, several algorithms have been proposed to partially solve this problem. We show the relations between them, leading to the following conclusion: the Markov Monoid Algorithm is the most correct algorithm known to (partially) solve the value 1 problem.

Keywords

Cite

@article{arxiv.1410.3770,
  title  = {What is known about the Value 1 Problem for Probabilistic Automata?},
  author = {Nathanaël Fijalkow},
  journal= {arXiv preprint arXiv:1410.3770},
  year   = {2014}
}
R2 v1 2026-06-22T06:23:16.605Z