are established, the recognizer when it observes A can conduct a search leading to the maximizing word string W. In the case of an artificial grammar, such as the New Raleigh grammar, the model P(W) is in fact equal to the actual probability P(W).
furthermore, because the set S of word strings W over which we maximize can be listed, the difficulty of the task can be measured approximately (because the acoustic similarity of words is not taken into account) by entropy: because the participants in the ARPA project introduced the false measure "branching factor" (which was the arithmetic mean of the out-of-state branching of their finite-state grammar), we replaced H(W) as a measure of difficulty by perplexity, defined by PP 2 H (W) It turned out that the New Raleigh grammar had approximate perplexity 7 whereas the Resource Management grammar had 2.