A new dichotomic algorithm for the uniform random generation of words in regular languages

We present a new algorithm for generating uniformly at random words of any regular language L. When using floating point arithmetics, its bit-complexity is O(qlg2n) in space and O(qnlg2n) in time, where n stands for the length of the word, and q stands for the number of states of a finite deterministic automaton of L. We implemented the algorithm and compared its behavior to the state-of-the-art algorithms, on a set of large automata from the VLTS benchmark suite. Both theoretical and experimental results show that our algorithm offers an excellent compromise in terms of space and time requirements, compared to the known best alternatives. In particular, it is the only method that can generate long paths in large automata.