### What is known about the Value 1 Problem for Probabilistic Automata? [article]

Nathanaël Fijalkow
<span title="2014-10-13">2014</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
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
more &raquo; ... sion: the Markov Monoid Algorithm is the most correct algorithm known to (partially) solve the value 1 problem.
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