The dissertation of Andreas Stolcke is approved: University of ...

,,,CHAPTER 6. EFFICIENT PARSING WITH STOCHASTIC CONTEXT-FREE GRAMMARS 153Its chart is disjoint from the one used by the parent instance. It cannot use states from the parent¡chart, except those explicitly passed to it (see below). Conversely, when finished, the parent has accessonly to those states returned explicitly by the child instance. 16 (The first restriction prevents parsing ofconstituents that cross the left phrase boundary, while the second restriction prevents a violation of theright phrase boundary.)The chart of the child is initialized with all incomplete states from the parent’s state set at the start¡position of the substring.The child returns to the parent all (and only) the complete states from its last state set. The parent adds¡the returned states to the state set at the position immediately following the end of the substring, usingit as the input for its own completion procedure.Thus the recursive parser invocation and the following completion step replaces the usual predictionscanning-completioncycle for the entire bracketed substring. After the child returns, the¡parentcontinues processing regular input symbols, or other bracketed substrings.Needless to say, the child parser instance may itself call on recursive instances to deal with nested¡bracketings.This recursion scheme is efficient in that it never explicitly rejects a parse that would be inconsistentwith the bracketing. Instead it only considers those parses that are consistent with the bracketing, whilecontinuing to make use of top-down information like a standard Earley parser.Processing bracketed strings requires no modification to the computation of probabilities. Probabilitiesare passed between parent and child as part of states, and processed as before. The recursive controlstructure simply constrains the set of Earley paths considered by the parser, thereby affecting the probabilitiesindirectly. For example, ambiguous strings may end up with lower inner probabilities because somederivations are inconsistent with the bracketing.Only the forward pass is directly affected by the bracketing. Both the Viterbi procedure (Section6.5.1) and the reverse completion pass (Section 6.5.2) only examine the states already in the chart. Theyare therefore automatically constrained by the bracketing.Complexity To assess the complexity benefit of bracketing we can extend the analysis of Section 6.4.9,making use of the recursive structure of the algorithm.In the standard parsing scheme, the time ð G3complexity is 0 for an input of length . Hence, in,