# On Stochastic Automata over Monoids

arXiv: https://arxiv.org/abs/2002.01214 · HTML: https://mlsanity.com/paper/2002.01214/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Feb 2020.

## Built on by (most cited first, 1 of 1)

- [On the Theory of Stochastic Automata](https://mlsanity.com/paper/2103.14423/) (2021)

## Abstract (arXiv)

Stochastic automata over monoids as input sets are studied. The well-definedness of these automata requires an extension postulate that replaces the inherent universal property of free monoids. As a generalization of Turakainen's result, it will be shown that the generalized automata over monoids have the same acceptance power as their stochastic counterparts. The key to homomorphisms is a commuting property between the monoid homomorphism of input states and the monoid homomorphism of transition matrices. Closure properties of the languages accepted by stochastic automata over monoids are investigated. matrices. Closure properties of the languages accepted by stochastic automata over monoids are investigated.