LING571

Homework 1

Due 10/6/05

Read J&M Chapter 9 before working on Ex 1-3.

1. (35 pts) Finish Exercise 9.2 on Page 355 in J&M, using the following tagset:

(a) POS tags:

- N, V, P (preposition), Adj, Adv, Pron, Det, Conj

- CD (cardinal number), PDT (pre-determiner), RP (particle), etc.

(b) Syntactic tags: NP, VP, PP, AdjP, AdvP, S, etc.

2. (20 pts) List ten sentences that can be generated by the following context-free grammar:

(a) S => NP VP

(b) NP => N

(c) NP => Det N

(d) NP => NP PP

(e) VP => V NP

(f) VP => VP PP

(g) PP => P NP

(h) N => book / Mary / store / card

(i) Det => the

(j) V => bought / is / was

(k) P => in/with

3. (15 pts) Does the grammar in Ex 2 allow ungrammatical sentences? If so, list two of them. How can you modify the grammar so that the two sentences that you have chosen would no longer be possible under the new grammar?

4. (30 pts) Given sentences (a)-(d):

(a) The/Det car/N killed/V the/Det duck/N

(b) The/Det duck/N died/V under/P her/Pron car/N

(c) We/Pron duck/V under/P the/Det car/N

(d) We/Pron retrieve/V the/Det poor/Adj duck/N

Calculate the following probabilities:

1. P (w₂=duck | w₁= the)

2. P (w₁=the | w₂ = duck)

3. P (w₂ = duck | t₂ = N)

4. P (w₂ = duck | t₁ = Det)

5. P (t₂ = V | t₁ = N)

6. P (t₂ = P | t₁ = V, t₀ = N)