Learning a Random DFA from Uniform Strings and State Information.

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.