Randomized Parallel Algorithms for the Homing Sequence Problem

{ Homing sequences play an important role in the testing of nite state systems and have been recently used in learning algorithms due to Rivest and Schapire 17] and Freund et al. 4]. It is well-known that every minimal DFA has a homing sequence of length O(n 2) which can be constructed sequentially in time O(n 3). But no eecient parallel algorithm was known for this problem. In this work, we present two RNC algorithms of time complexity O(log 2 n) for this problem. We show that one of our RNC algorithms produces a homing sequence of length O(n log 2 n) for almost all DFA's with n states using a random model of Traktenbrot and Barzdin. We also discuss connections between the homing sequence problem and other problems in the eld of hardware fault-testing and protocol veriication.