Learning Probabilistic Finite Automata
Colin de la Higuera and Jose Oncina
Lecture Notes in Artificial Intelligence 2004. ISSN 0302-9743

## Abstract

Stochastic deterministic finite automata have been introduced and are used in a variety of settings. We report here a number of results concerning the learnability of these finite state machines. In the setting of identification in the limit with probability one, we prove that stochastic deterministic finite automata cannot be identified from only a polynomial quantity of data. If concerned with approximation results, they become \textsc{Pac}-learnable if the $L_{\infty}$ norm is used. We also investigate queries that are sufficient for the class to be learnable.