## Using the grammar in Example 3.2 [p.117]*, draw a parse tree for each of the three following statements: Attach your parse trees as a single jpg or gif file.

### computer science

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1Question 1

Using the grammar in Example 3.2 [p.117]*, draw a parse tree for each of the three following statements:

Attach your parse trees as a single jpg or gif file.

A = A * (B + (C * A))

B = C * (A * C + B)

A = A * (B + (C))

### Question 2

Using the grammar in Example 3.2 [p.117]*, show a sentential form leftmost derivation for each of the three following statements.

Write your derivation steps in the answer space below:

Note: These are the same three statements as the previous questions.

A = A * (B + (C * A))

B = C * (A * C + B)

A = A * (B + (C))

### Question 3

Using the grammar in Example 3.4 [p.120]*, draw a parse tree for each of the four following statements:

Attach your parse trees as a single jpg or gif file.

A = ( A + B ) * C

A = B + C + A

A = A * (B + C)

A = B * (C * (A + B))

### Question 4

Using the grammar in Example 3.4 [p.120]*, show a sentential form leftmost derivation for each of the four following statements.

Write your derivations in the answer space below:

Note: These are the same four statements as the previous questions.

A = ( A + B ) * C

A = B + C + A

A = A * (B + C)

A = B * (C * (A + B))

### Question 5

Prove that the following BNF grammar is ambiguous.

Attach your parse trees as a single jpg or gif file.

<S> → <A>

<A> → <A> + <A> | <id>

<id> → a | b | c

### Question 6

Describe, in English, the language defined by the following grammar:

SABC

AaA | a

BbB | b
CcC | c

### Question 7

Consider the following grammar:

<S> → <A> a <B> b

<A> → <A> b | b

<B> → a <B> | a

Which of the following strings are in the language generated by this grammar?

 bbaab baab bbaaaaa bbbab

### Question 8

Consider the following grammar:

S →  aScB | A | b

A →  cA | c

B →  d | A

Which of the following sentences are in the language generated/recognized by this grammar?

 acccbd acd acccbcc accc cd abcd

### Question 9

Convert the following EBNF rules to BNF:

SA{bA}

Aa[b]A

Note: These rules are an incomplete grammar. You are responsible only for converting the given rules (partial grammar).

### Question 10

Write EBNF descriptions (i.e. rules) for the a Java class definition header statement.

Begin with the start symbol <class_header>.

Use the non-terminal <class_name> for the user-defined name of the class

You do not have to include a LHS rule which defines valid naming conventions to expand the <class_name> non-terminal