Abstract

Approximate inference of finite state machines from sparse labeled examples has been proved NP-hard when an adversary chooses the target machine and the training set [Ang78, KV89, PW89]. We have, however, empirically found that DFA's are approximately learnable from sparse data when the target machine and training set are selected at random. 1 A Greedy Learning Algorithm Trakhtenbrot and Barzdin described the following polynomial time algorithm for constructing the smallest DFA consistent with a complete labeled training set [TB73]. The input to the algorithm is the prefix-tree acceptor which directly embodies the training set. This tree is collapsed into a smaller graph by merging all pairs of states that represent compatible mappings from string suffixes to labels. The algorithm contains two nested loops. In the outer loop, each node i is visited in breadth-first order starting at the tree's root. In the inner loop, each node j between the root and node i \Gamma 1 is evaluated for ...

Citations

200	Random number generators: good ones are hard to find - Park, Miller - 1988
88	On the complexity of minimum inference of regular sets - Angluin - 1978
75	Finite Automata, Behavior and Synthesis - Trakhtenbrot, Barzdin - 1973
11	The minimum DFA consistency problem cannot be approximated within any polynomial - Pitt, Warmuth - 1989
2	Inference of Sequential Machines from Sample Computations - Veelenturf - 1978