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# Characterisation of an Algebraic Algorithm for Probabilistic Automata

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LIPIcs.STACS.2016.34.pdf
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## Cite As

Nathanaël Fijalkow. Characterisation of an Algebraic Algorithm for Probabilistic Automata. In 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 47, pp. 34:1-34:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.STACS.2016.34

## Abstract

We consider the value 1 problem for probabilistic automata over finite words: it asks whether a given probabilistic automaton accepts words with probability arbitrarily close to 1. This problem is known to be undecidable. However, different algorithms have been proposed to partially solve it; it has been recently shown that the Markov Monoid algorithm, based on algebra, is the most correct algorithm so far. The first contribution of this paper is to give a characterisation of the Markov Monoid algorithm. The second contribution is to develop a profinite theory for probabilistic automata, called the prostochastic theory. This new framework gives a topological account of the value 1 problem, which in this context is cast as an emptiness problem. The above characterisation is reformulated using the prostochastic theory, allowing to give a modular proof.
##### Keywords
• Probabilistic Automata
• Value 1 Problem
• Markov Monoid Algorithm
• Algebraic Algorithm
• Profinite Theory
• Topology in Computer Science

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