2. ๏ฝ We also want trees that cover the input
words.
๏ฝ Start with trees that link up with the words
๏ฝ Then work your way up from there to larger
and larger trees.
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4. ๏ฝ Top-down
โฆ Only searches for trees that can be Sโs
โฆ But also suggests trees that are not consistent with
any of the words
๏ฝ Bottom-up
โฆ Only forms trees consistent with the words
โฆ But suggests trees that make no sense globally
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5. ๏ฝ Which node to try to expand next
๏ฝ Which grammar rule to use to expand a
node
๏ฝ One approach: exhaustive search of the
space of possibilities
๏ฝ Not feasible
โฆ Time is exponential in the number of non-
terminals
โฆ LOTS of repeated work, as the same constituent is
created over and over (shared sub-problems)
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6. ๏ฝ DP search methods fill tables with partial
results and thereby
โฆ Avoid doing avoidable repeated work
โฆ Solve exponential problems in polynomial time
(well, no not really โ weโll return to this point)
โฆ Efficiently store ambiguous structures with
shared sub-parts.
๏ฝ Weโll cover two approaches that roughly
correspond to bottom-up and top-down
approaches.
โฆ CKY
โฆ Earley โ we will mention this, not cover it in
detail
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