Lecture 5 Dec 2006

Looks like I turned off the tablet without saving the screen capture. Here's what we did:

• Grammar/automaton optimization algorithms
  • Big idea: first compute logical dependency structure, then walk that structure
  • DFA minimization: can be made to run in O(n^2) time, rather than O(N^4) algorithm we saw last class
  • removing useless symbols from context-free grammars: can run in linear time
• Parsing algorithms for context-free languages
  • Big idea: dynamic programming (solve each sub-problem only once)
  • CYK parsing algorithm: see slides from last term
  • CYK is O(n^3) for an input of length n and requires grammar in Chomsky-normal form.
  • Earley algorithm (similar but slightly harder to present) is still general, but doesn't require Chomsky-normal form and runs faster on "nice" grammars. E.g. O(n) on many used in practice.
  • Algorithms used in tools like Yacc (LL, LR, LALR, SLR) are parse restricted types types of grammars, but include most required by applications and run in O(n) time.
  • Key ideas in faster algorithms include a word or two of look-ahead, also working downwards from the start symbol rather than upwards from the input words.
• Curious? See sections 4.3, 4.4 and 7.4 of the Hopcroft, Motwani, and Ullman text on reserve in the Engineering library.
• We also did ICES course evals.