Learning a Random DFA from Uniform Strings and State Information

Abstract

Deterministic finite automata (DFA) have long served as a fundamental computational model in the study of theoretical computer science, and the problem of learning a DFA from given input data is a classic topic in computational learning theory. In this paper we study the learnability of a random DFA and propose a computationally efficient algorithm for learning and recovering a random DFA from uniform input strings and state information in the statistical query model. A random DFA is uniformly generated: for each state-symbol pair $(q \in Q, \sigma \in \Sigma )$, we choose a state $q' \in Q$ with replacement uniformly and independently at random and let $\varphi (q, \sigma ) = q'$, where Q is the state space, $\Sigma$ is the alphabet and $\varphi$ is the transition function. The given data are string-state pairs (x, q) where x is a string drawn uniformly at random and q is the state of the DFA reached on input x starting from the start state $q_0$. A theoretical guarantee on the maximum absolute error of the algorithm in the statistical query model is presented. Extensive experiments demonstrate the efficiency and accuracy of the algorithm.