Some challenges for context-free grammars:

Agreement: leads to multiplication of rules to handle number, case

• "those flights stop in Chicago" vs. "that flight stops in Chicago"
• "they served me dinner" vs. "I was served dinner"

Subcategorization: leads to multiplication of rules to handle verb types

• "it left" vs. "it serves dinner" vs. "you said there were two flights"

Relations between sentences: each "version" has the same number and subcategorization patterns, leading to redundancies

• "that flight stops in Chicago" vs. "does that flight stop in Chicago?" (yes-no questions)
• "the flight arrives at 9:00" vs. "what time does the flight arrive?" (wh-questions)
• "they serve dinner on that flight" vs. "dinner is served on that flight" (passive)
• "who serves dinner" vs. "who did you say serves dinner?" (long-distance dependencies)

Parsing with CFGs:

"Search through the speace of all possible parse trees to find the correct parse tree for the sentence"

Top-down: start building trees starting with S (by expanding the left sides of rules) until you get a tree or trees that fit

Bottom-up: starting from words and tags, find node labels that fit (by matching the right sides of rules)

Top-down with bottom-up filtering: check the "left corner" (first item) before considering an expansion. NPs start with Det or N; S with Det, N, Aux, V; VP with V; etc.