Maximal Derivations for Probabilistic Strings in Stochastic Languages

A probabilistic string is a sequence of probability vectors. Each vector specifies a probability distribution over the possible symbols at its location in the string. In a probabilistic grammar a probability is assigned to every derivation. Given a probabilistic string and a probabilistic grammar the concept of a maximal derivation is defined. Algorithms for finding the maximal derivation for probabilistic finite state and linear grammars are given. The case where a waveform can be segmented into several possible probabilistic strings is also considered.