the process only returns the references of the actual result and eventually speeds up the overall computation. During updating the memotable, the memoization process groups the (potentially exponential) ambiguous results and ensures the polynomial space requirement. Frost, Hafiz and Callaghan also described the implementation of the algorithm in PADL’08 as a set of higher-order functions (called parser combinators) in Haskell, which enables the construction of directly executable specifications of CFGs as language processors. The importance of their polynomial algorithm’s power to accommodate ‘any form of ambiguous CFG’ with top-down parsing is vital with respect to the syntax and semantics analysis during natural language processing. The X-SAIGA site has more about the algorithm and implementation details. While Norvig increased the power of the parser through memoization, the augmented parser was still as time complex as Earley's algorithm, which demonstrates a case of the use of memoization for something other than speed optimization. Johnson and Dörre demonstrate another such non-speed related application of memoization: the use of memoization to delay linguistic constraint resolution to a point in a parse where sufficient information has been accumulated to resolve those constraints. By contrast, in the speed optimization application of memoization, Ford demonstrated that memoization could guarantee that parsing expression grammars could parse in linear time even those languages that resulted in worst-case backtracking behavior. Consider the following grammar: S → (A c) | (B d) A → X (a|b) B → X b X → x [X] (Notation note: In the above example, the production S → (A c) | (B d) reads: "An S is either an A followed by a c or a B followed by a d." The production X → x [X] reads "An X is an x followed by an optional X.") This grammar generates one of the following three variations of string: xac, xbc, or xbd (where x here is understood to mean one or more x's.) Next, consider how this grammar, used as a parse specification, might effect a top-down, left-right parse of the string xxxxxbd: The rule A will recognize xxxxxb (by first descending into X to recognize one x, and again descending into X until all the x's are consumed, and then recognizing the b), and then return to S, and fail to recognize a c. The next clause of S will then descend into B, which in turn again descends into X and recognizes