THEORY OF COMPUTATION SERIES LECTURES

1. Prof.Neeraj Bhargava
Abhishek Kumar
Department of Computer Science
School of Engineering & System Sciences,
MDS, University Ajmer, Rajasthan, India
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2.  We also want trees that cover the input
words.
 Start with trees that link up with the words
 Then work your way up from there to larger
and larger trees.
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3. 3

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