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QUESTION: 1

Assume the statements S1 and S2 given as:

S1: Given a context free grammar, there exists an algorithm for determining whether L (G) is infinite.

S2: There exists an algorithm to determine whether two context free grammars generate the same language.

Which of the following is true?

Solution:

The proof of S1 can be seen in various book of theory of computation but s2 is a problem of category undecidable so a contradiction to this assumption can be easily obtained.

QUESTION: 2

If P & R are regular and also given that if PQ=R, then

Solution:

If two regular languages when combined do not always produce a regular language.

QUESTION: 3

Which of the following conversion is not possible (algorithmically)?

Solution:

Not every NDPDA has an equivalent deterministic PDA.

QUESTION: 4

Consider the grammar given below E? E+E | E*E | E-E | E/E | E^E | (E) | id Assume that + and ^ have the same but least precedence, * and / have the next higher precedence but the same precedence and finally ^ has the highest precedence. Assume + and ^ associate to the left like * and / and that ^ associates to the right. Choose the correct for the ordered pairs (^,^) , (-,-) , (+,+) , (*,*) in the operator precedence table constructed for the grammar

Solution:

This relation is established of basis of the precedence of operators.

QUESTION: 5

Recursively enumerable languages are not closed under:

Solution:

Recursive languages are closed under the following operations.

The Kleene star L * of L

the concatenation L * o P of L and P

the union L U P

the intersection L ∩ P.

QUESTION: 6

Grammar that produce more than one Parse tree for same sentence is:

Solution:

an ambiguous grammar is one for which there is more than one parse tree for a single sentence.

QUESTION: 7

Automaton accepting the regular expression of any number of a ‘ s is:

Solution:

It gives any number of a’s.

QUESTION: 8

Grammars that can be translated to DFAs:

Solution:

Right linear grammar can be translated to the DFAs.

QUESTION: 9

The language accepted by a Push down Automata:

Solution:

A known fact that type 2 grammar is accepted by PDA.

QUESTION: 10

Given the following statements: (i) Recursive enumerable sets are closed under complementation. (ii) Recursive sets are closed under complements. Which is/are the correct statements?

Solution:

Recursive languages are closed under the following operations.

The Kleene star L * of L

the concatenation L * o P of L and P

the union L U P

the intersection L ∩ P.

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