Exercise 3 Show that each of the following grammars is ambiguous. (To show that a grammar is ambiguous, you must demonstrate that it can generate two parse trees for the same string.) a. The grammar G4, repeated here: G4: = + | + | ( ) |a|b|c b. This grammar: := | ::= wilma | betty | ::= fred | barney | c. The following grammar for strings of balanced parentheses. (A language of any number of different kinds of balanced parentheses is called a Dyck lan- guage. This type of language plays an interesting role in the theory of formal languages.)

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Exercise 3 Show that each of the following grammars is ambiguous. (To show
that a grammar is ambiguous, you must demonstrate that it can generate two parse
trees for the same string.)
a. The grammar G4, repeated here:
G4: <exp>:= <exp> + <exp>
| <exp>
<exp>
| (<exp> )
|a|b|c
b. This grammar:
<person>:= <woman> | <man>
<woman> ::= wilma | betty | <empty>
<man> ::= fred | barney | <empty>
c. The following grammar for strings of balanced parentheses. (A language of
any number of different kinds of balanced parentheses is called a Dyck lan-
guage. This type of language plays an interesting role in the theory of formal
languages.)
<S>
<S> <S> <S>) 10
d. This grammar:
<s> :: = <round> <square> | <outer>
<round>:= (<round> ) | 0
<square> ::= [ <square> 1 | []
<outer> : <outer> ] |
<inner> ]
<inner> ::=) <inner> [ ) [
Exercise 4 For each of the grammars in Exercise 3 except the last, give an unam-
biguous grammar for the same language. (The last grammar in that exercise is a
classic example of an inherently ambiguous grammar-it cannot be fixed!)
Transcribed Image Text:Exercise 3 Show that each of the following grammars is ambiguous. (To show that a grammar is ambiguous, you must demonstrate that it can generate two parse trees for the same string.) a. The grammar G4, repeated here: G4: <exp>:= <exp> + <exp> | <exp> <exp> | (<exp> ) |a|b|c b. This grammar: <person>:= <woman> | <man> <woman> ::= wilma | betty | <empty> <man> ::= fred | barney | <empty> c. The following grammar for strings of balanced parentheses. (A language of any number of different kinds of balanced parentheses is called a Dyck lan- guage. This type of language plays an interesting role in the theory of formal languages.) <S> <S> <S> <S>) 10 d. This grammar: <s> :: = <round> <square> | <outer> <round>:= (<round> ) | 0 <square> ::= [ <square> 1 | [] <outer> : <outer> ] | <inner> ] <inner> ::=) <inner> [ ) [ Exercise 4 For each of the grammars in Exercise 3 except the last, give an unam- biguous grammar for the same language. (The last grammar in that exercise is a classic example of an inherently ambiguous grammar-it cannot be fixed!)
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We have explain exercise 4 because it consists of question exercise3 a, b , c  and d part but we have explain in first three from the part in the brief explanation.

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