Automata Theory Multiple Choice Questions on “DPDA and Ambiguous Grammars”.
1. CFGs are more powerful than:
a) DFA
b) NDFA
c) Mealy Machine
d) All of the mentioned
Answer: d
Clarification:
Context-free grammars are strictly more powerful than regular expressions:
1) Any language that can be generated using regular expressions can be generated by a context-free grammar.
2) There are languages that can be generated by a context-free grammar that cannot be generated by any regular expression.
As a corollary, CFGs are strictly more powerful than DFAs and NDFAs.
2. State true or false:
S-> 0S1|01
Statement: No regular expression exists for the given grammar.
a) true
b) false
Answer: a
Clarification: The grammar generates a language L such that L={0n1n|n>=1} which is not regular. Thus, no regular expression exists for the same.
3. For the given set of code, the grammar representing real numbers in Pascal has error in one of the six lines. Fetch the error.
(1) ->
(2) -> | epsilon
(3) -> | epsilon
(4) -> ‘E’ | epsilon
(5) -> + | – | epsilon
(6) -> 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
a) 3
b) 4
c) 2
d) No errors
Answer: a
Clarification:
–>
–> | epsilon
–> ‘.’ | epsilon
–> ‘E’ | epsilon
–> + | – | epsilon
–> 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
4. Which among the following is incorrect with reference to a derivation tree?
a) Every vertex has a label which is a terminal or a variable.
b) The root has a label which can be a terminal.
c) The label of the internal vertex is a variable.
d) None of the mentioned
Answer: b
Clarification: The root or interms of the grammar, starting variable can not be a terminal.
5. Let G=(V, T, P, S)
where a production can be written as:
S->aAS|a
A->SbA|ba|SS
Which of the following string is produced by the grammar?
a) aabbaab
b) aabbaa
c) baabab
d) None of the mentioned
Answer: b
Clarification: The step wise grammar translation can be written as:
aAS->aSbaA->aabAS->aabbaa
6. Statement 1: Ambiguity is the property of grammar but not the language.
Statement 2: Same language can have more than one grammar.
Which of the following options are correct with respect to the given statements?
a) Statement 1 is true but statement 2 is false
b) Statement 1 is false but statement 2 is true
c) Both the statements are true
d) Both the statements are false
Answer: c
Clarification: One language can more than one grammar. Some can be ambiguous and some cannot.
7. Which of the following are non essential while simplifying a grammar?
a) Removal of useless symbols
b) Removal of unit productions
c) Removal of null production
d) None of the mentioned
Answer: d
Clarification: Here are some process used to simplify a CFG but to produce an equivalent grammar:
a) Removal of useless symbols(non terminal) b) Removal of Unit productions and c) Removal of Null productions.
8. Which of the following are context free language?
a) L={aibi|i>=0}
b) L={wwr| w is a string and r represents reverse}
c) Both (a) and (b)
d) one of the mentioned
Answer: a
Clarification: None.
9. The language L ={ai2bi|i>=0} is:
a) recursive
b) deterministic CFL
c) regular
d) Two of the mentioned is correct
Answer: d
Clarification: The language is recursive and every recursive language is a CFL.
10. L->rLt|tLr|t|r
The given grammar produces a language which is:
a) All palindrome
b) All even palindromes
c) All odd palindromes
d) Strings with same begin and end symbols
Answer: c
Clarification: As there exists no production for the palindrome set, even palindromes like abba, aabbaa, baaaaaab, etc will not be generated.