# Theory of Computation and Compilers - Context free languages

>>>>>>>>Context free languages

• A

⊕ is left associative while * is right associative  • B

Both ⊕ and * are left associative  • C

⊕ is right associative while * is left associative  • D

None of these  • A

S --> Sa | b  • B

S --> aSb | ab  • C

S --> abX, X --> cY, Y --> d | aX  • D

None of these  • Option : B
• Explanation :
Option (B) generates the set {an bn, n=1,2,3 ....} which is not regular, Option (A) is left linear where as option (C) is right linear .

• A

2x - 1  • B

2x  • C

2x + 1  • D

None of these  • A

A = { If an bn  | n = 0,1, 2, 3 ..} is regular language  • B

Set B of all strings of equal number of a's and b's defines a regular language  • C

L (A* B*)∩ B gives the set A  • D

None of these  • Option : C
• Explanation :
If we include A and B in a set and if we write A* it means except then A i.e. B same as B* means except then B i.e.A so if we intersect (A*B*) and B then get A because in any regular language
if we write A-B then A-B=A intersection B' so if we intersect A and B means A-B So intersection of (A*B*) and B = (BA) intersection B means (BA)-B' and B'=A so (BA) intersection(A)=A So ans is (C)

## Description

Syllabus covered in this section is-

• Regular languages and finite automata
• Context free languages and Push-down automata
• Recursively enumerable sets and Turing machines
• Undecidability, NPcompleteness
• Models of computation-Finite Automata
• Pushdown Automata
• Non-detenninism and NFA. DPDA and PDAs and Languages accepted by these Structures
• Grammars, Languages,
• Non- computability and Examples of non-computable problems

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