Time and Space Complexity of Top-down Parsing
When top-down parser tries to parse an ambiguous input with respect to an ambiguous CFG, it may need exponential number of steps (with respect to the length of the input) to try all alternatives of the CFG in order to produce all possible parse trees, which eventually would require exponential memory space. The problem of exponential time complexity in top-down parsers constructed as sets of mutually recursive functions has been solved by Norvig in 1991. His technique is similar to the use of dynamic programming and state-sets in Earley's algorithm (1970), and tables in the CYK algorithm of Cocke, Younger and Kasami.
The key idea is to store results of applying a parser p at position j in a memotable and to reuse results whenever the same situation arises. Frost, Hafiz and Callaghan also use memoization for refraining redundant computations to accommodate any form of CFG in polynomial time (Θ(n4) for left-recursive grammars and Θ(n3) for non left-recursive grammars). Their top-down parsing algorithm also requires polynomial space for potentially exponential ambiguous parse trees by 'compact representation' and 'local ambiguities grouping'. Their compact representation is comparable with Tomita’s compact representation of bottom-up parsing.
Using PEG's, another representation of grammars, packrat parsers provide an elegant and powerful parsing algorithm. See Parsing expression grammar.
Read more about this topic: Top-down Parsing
Famous quotes containing the words time, space and/or complexity:
“As yesterday and the historical ages are past, as the work of today is present, so some flitting perspectives and demi-experiences of the life that is in nature are in time veritably future, or rather outside of time, perennial, young, divine, in the wind and rain which never die.”
—Henry David Thoreau (1817–1862)
“With sturdy shoulders, space stands opposing all its weight to nothingness. Where space is, there is being.”
—Friedrich Nietzsche (1844–1900)
“In times like ours, where the growing complexity of life leaves us barely the time to read the newspapers, where the map of Europe has endured profound rearrangements and is perhaps on the brink of enduring yet others, where so many threatening and new problems appear everywhere, you will admit it may be demanded of a writer that he be more than a fine wit who makes us forget in idle and byzantine discussions on the merits of pure form ...”
—Marcel Proust (1871–1922)