Implicitly Intersecting Weighted Automata using Dual Decomposition

Michael J. Paul, Jason Eisner

Abstract: We propose an algorithm to find the best path through an intersection of arbitrarily many weighted automata, without actually performing the intersection. The algorithm is based on dual decomposition: the automata attempt to agree on a string by communicating about features of the string. We demonstrate the algorithm on the Steiner consensus string problem, both on synthetic data and on consensus decoding for speech recognition. This involves implicitly intersecting up to 100 automata.