Question 1

The number of tokens in the following C statement is (GATE 2000) printf("i = %d, &i = %x", i, &i);

Accepted Answer

A) 3 
B) 26 
C) 10 
D) 21 
A) 3 
B) 26 
C) 10 
D) 21 C

Question 2

Which one of the following is FALSE?

Accepted Answer

A) There is unique minimal DFA for every regular language 
B) Every NFA can be converted to an equivalent PDA. 
C) Complement of every context-free language is recursive. 
D) Every nondeterministic PDA can be converted to an equivalent deterministic PDA. 
A) There is unique minimal DFA for every regular language 
B) Every NFA can be converted to an equivalent PDA. 
C) Complement of every context-free language is recursive. 
D) Every nondeterministic PDA can be converted to an equivalent deterministic PDA. D

Question 3

Which of the following statements is false?

Accepted Answer

A) Every context-sensitive language is recursive. 
B) The set of all languages that are not recursively enumerable is countable. 
C) The family of recursively enumerable languages is closed under union. 
D) The families of recursively enumerable and recursive languages are closed under reversal 
A) Every context-sensitive language is recursive. 
B) The set of all languages that are not recursively enumerable is countable. 
C) The family of recursively enumerable languages is closed under union. 
D) The families of recursively enumerable and recursive languages are closed under reversal B

Question 4

Let S and T be language over ={a,b} represented by the regular expressions (a+b*)* and (a+b)*, respectively. Which of the following is true?

Accepted Answer

A) ScT (S is a subset of T) 
B) TcS (T is a subset of S) 
C) S=T 
D) SnT=Ø 
A) ScT (S is a subset of T) 
B) TcS (T is a subset of S) 
C) S=T 
D) SnT=Ø

Question 5

Which of the following are decidable?
I. Whether the intersection of two regular languages is infinite
II. Whether a given context-free language is regular
III. Whether two push-down automata accept the same language
IV. Whether a given grammar is context-free

Accepted Answer

A) I and II 
B) I and IV 
C) II and III 
D) II and IV 
A) I and II 
B) I and IV 
C) II and III 
D) II and IV

Question 6

If L and L' are recursively enumerable, then L is

Accepted Answer

A) regular 
B) context free 
C) context sensitive 
D) recursive 
A) regular 
B) context free 
C) context sensitive 
D) recursive

Question 7

Consider the following two statements:
S1: { 0^2n |n >= l} is a regu1ar language
S2: { 0^m 0^n 0^(m+n) l m >= 1 and n >= 2} is a regu1ar language
Which of the following statements is correct?

Accepted Answer

A) Only S1 is correct 
B) Only S2 is correct 
C) Both S1 and S2 are correct 
D) None of S1 and S2 is correct 
A) Only S1 is correct 
B) Only S2 is correct 
C) Both S1 and S2 are correct 
D) None of S1 and S2 is correct

Question 8

For S ? (0 + 1) * let d(s) denote the decimal value of s (e.g. d(101) = 5). Let L = {s ? (0 + 1)* d(s)mod5 = 2 and d(s)mod7 != 4}. Which one of the following statements is true?

Accepted Answer

A) L is recursively enumerable, but not recursive 
B) L is recursive, but not context-free 
C) L is context-free, but not regular 
D) L is regular 
A) L is recursively enumerable, but not recursive 
B) L is recursive, but not context-free 
C) L is context-free, but not regular 
D) L is regular

Question 9

Consider the following identities for regular expressions: (a) (r + s)* = (s + r)* (b) (r*)* = r* (c) (r* s*)* = (r + s)* Which of the above identities are true?

Accepted Answer

A) (a) and (b) only 
B) (b) and (c) only 
C) (c) and (a) only 
D) (a), (b) and (c) 
A) (a) and (b) only 
B) (b) and (c) only 
C) (c) and (a) only 
D) (a), (b) and (c)

Question 10

Which of the following are decidable ?
1) whether the intersection of two regular language is infinite.
2) whether a give context free language is regular
3) whether two push down automata accept the same language.
4) whether a given grammar is context free

Accepted Answer

A) 1 and 2 
B) 1 and 4 
C) 2 and 3 
D) 2 and 4 
A) 1 and 2 
B) 1 and 4 
C) 2 and 3 
D) 2 and 4

Question 11

In some programming languages, an identifier is permitted to be a letter followed by any number of letters or digits. If L and D denotes the set of letters and digit respectively. Which of the following expression defines an identifier?

Accepted Answer

A) (L + 
D)  * 
B) (L.
D)  * 
C) L(L + 
D)  * 
D) L(L.
D)  * 
A) (L + 
D)  * 
B) (L.
D)  * 
C) L(L + 
D)  * 
D) L(L.
D)  *

Question 12

Let  be the encoding of a Turing machine as a string over ?= {0, 1}. Let L = {  |M is a Turing machine that accepts a string of length 2014 }. Then, L is

Accepted Answer

A) decidable and recursively enumerable 
B) undecidable but recursively enumerable 
C) undecidable and not recursively enumerable 
D) decidable but not recursively enumerable 
A) decidable and recursively enumerable 
B) undecidable but recursively enumerable 
C) undecidable and not recursively enumerable 
D) decidable but not recursively enumerable

Question 13

Which of the following pairs have DIFFERENT expressive power?

Accepted Answer

A) Deterministic finite automata (DF
A)  and Non-Deterministic finite automata(NF
A)  
B) Deterministic push down automata (DPD
A)  and Non-deterministic pushdown automata 
C) Deterministic single-tape Turing machine and Non-deterministic single-tape Turing Machine 
D) Single-tape Turing machine and multi-tape Turing machine 
A) Deterministic finite automata (DF
A)  and Non-Deterministic finite automata(NF
A)  
B) Deterministic push down automata (DPD
A)  and Non-deterministic pushdown automata 
C) Deterministic single-tape Turing machine and Non-deterministic single-tape Turing Machine 
D) Single-tape Turing machine and multi-tape Turing machine

Question 14

The regular grammar for the language L = {anbm | n + m is even} is given by

Accepted Answer

Question 15

Which of the following statements in true?

Accepted Answer

A) If a language is context free it can always be accepted by a deterministic push-down automaton 
B) The union of two context free languages is context free 
C) The intersection of two context free languages is context free 
D) The complement of a context free language is context free 
A) If a language is context free it can always be accepted by a deterministic push-down automaton 
B) The union of two context free languages is context free 
C) The intersection of two context free languages is context free 
D) The complement of a context free language is context free

Question 16

Which of the following is true for the language {a^p} p is prine ?

Accepted Answer

A) It is not accepted by a turing machine 
B) It is regular but not context free 
C) It is context free but not regular 
D) It is neither regular nor context free but accepted by a turing machine 
A) It is not accepted by a turing machine 
B) It is regular but not context free 
C) It is context free but not regular 
D) It is neither regular nor context free but accepted by a turing machine

Question 17

Consider the following decision problems:
(P1) Does a given finite state machine accept a given string
(P2) Does a given context free grammar generate an infinite number of stings
Which of the following statements is true?

Accepted Answer

A) Both (P1) and (P2) are decidable 
B) Neither (P1) nor (P2) are decidable 
C) Only (P1) is decidable 
D) Only (P2) is decidable 
A) Both (P1) and (P2) are decidable 
B) Neither (P1) nor (P2) are decidable 
C) Only (P1) is decidable 
D) Only (P2) is decidable

Question 18

Let L denotes the language generated by the grammar S - OSO/00. Which of the following is true?

Accepted Answer

A) L = O 
B) L is regular but not O 
C) L is context free but not regular 
D) L is not context free 
A) L = O 
B) L is regular but not O 
C) L is context free but not regular 
D) L is not context free

Question 19

The number of strings of length 4 that are generated by the regular expression (0+1+|2+3+)*, where | is an alternation character and {+, *} are quantification characters, is:

Accepted Answer

A) 08 
B) 09 
C) 10 
D) 12 
A) 08 
B) 09 
C) 10 
D) 12

Question 20

Consider the CFG with {S,A,B) as the non-terminal alphabet, {a,b) as the terminal alphabet, S as the start symbol and the following set of production rules
S --> aB S --> bA
B --> b A --> a
B --> bS A --> aS
B --> aBB A --> bAA
Which of the following strings is generated by the grammar?

Accepted Answer

A) aaaabb 
B) aabbbb 
C) aabbab 
D) abbbba 
A) aaaabb 
B) aabbbb 
C) aabbab 
D) abbbba

The number of tokens in the following C statement is (GATE 2000) printf("i = %d, &i = %x", i, &i);

Which one of the following is FALSE?

Which of the following statements is false?

Let S and T be language over ={a,b} represented by the regular expressions (a+b) and (a+b)*, respectively. Which of the following is true?

Which of the following are decidable? I. Whether the intersection of two regular languages is infinite II. Whether a given context-free language is regular III. Whether two push-down automata accept the same language IV. Whether a given grammar is context-free

If L and L' are recursively enumerable, then L is

Consider the following two statements: S₁: { 0^2n |n >= l} is a regu1ar language S₂: { 0^m 0^n 0^(m+n) l m >= 1 and n >= 2} is a regu1ar language Which of the following statements is correct?

For S ? (0 + 1) * let d(s) denote the decimal value of s (e.g. d(101) = 5). Let L = {s ? (0 + 1)* d(s)mod5 = 2 and d(s)mod7 != 4}. Which one of the following statements is true?

Consider the following identities for regular expressions: (a) (r + s)* = (s + r)* (b) (r) = r* (c) (r* s) = (r + s)* Which of the above identities are true?

Which of the following are decidable ? 1) whether the intersection of two regular language is infinite. 2) whether a give context free language is regular 3) whether two push down automata accept the same language. 4) whether a given grammar is context free

In some programming languages, an identifier is permitted to be a letter followed by any number of letters or digits. If L and D denotes the set of letters and digit respectively. Which of the following expression defines an identifier?

Let be the encoding of a Turing machine as a string over ?= {0, 1}. Let L = { |M is a Turing machine that accepts a string of length 2014 }. Then, L is

Which of the following pairs have DIFFERENT expressive power?

The regular grammar for the language L = {anbm | n + m is even} is given by

Which of the following statements in true?

Which of the following is true for the language {a^p} p is prine ?

Consider the following decision problems: (P₁) Does a given finite state machine accept a given string (P₂) Does a given context free grammar generate an infinite number of stings Which of the following statements is true?

Let L denotes the language generated by the grammar S - OSO/00. Which of the following is true?

The number of strings of length 4 that are generated by the regular expression (0+1+|2+3+), where | is an alternation character and {+, } are quantification characters, is:

Consider the CFG with {S,A,B) as the non-terminal alphabet, {a,b) as the terminal alphabet, S as the start symbol and the following set of production rules S --> aB S --> bA B --> b A --> a B --> bS A --> aS B --> aBB A --> bAA Which of the following strings is generated by the grammar?

Formal Languages and Automata Theory: Part A

Compiler Construction and Parsing Algorithms

Compilation and Programming Languages

Filters

Exam 2: Formal Languages and Automata Theory: Part B

The number of tokens in the following C statement is (GATE 2000) printf("i = %d, &i = %x", i, &i);

Which one of the following is FALSE?

Which of the following statements is false?

Let S and T be language over ={a,b} represented by the regular expressions (a+b*)* and (a+b)*, respectively. Which of the following is true?

Which of the following are decidable? I. Whether the intersection of two regular languages is infinite II. Whether a given context-free language is regular III. Whether two push-down automata accept the same language IV. Whether a given grammar is context-free

If L and L' are recursively enumerable, then L is

Consider the following two statements: S1: { 0^2n |n >= l} is a regu1ar language S2: { 0^m 0^n 0^(m+n) l m >= 1 and n >= 2} is a regu1ar language Which of the following statements is correct?

For S ? (0 + 1) * let d(s) denote the decimal value of s (e.g. d(101) = 5). Let L = {s ? (0 + 1)* d(s)mod5 = 2 and d(s)mod7 != 4}. Which one of the following statements is true?

Consider the following identities for regular expressions: (a) (r + s)* = (s + r)* (b) (r*)* = r* (c) (r* s*)* = (r + s)* Which of the above identities are true?

Which of the following are decidable ? 1) whether the intersection of two regular language is infinite. 2) whether a give context free language is regular 3) whether two push down automata accept the same language. 4) whether a given grammar is context free

In some programming languages, an identifier is permitted to be a letter followed by any number of letters or digits. If L and D denotes the set of letters and digit respectively. Which of the following expression defines an identifier?

Let be the encoding of a Turing machine as a string over ?= {0, 1}. Let L = { |M is a Turing machine that accepts a string of length 2014 }. Then, L is

Which of the following pairs have DIFFERENT expressive power?

The regular grammar for the language L = {anbm | n + m is even} is given by

Which of the following statements in true?

Which of the following is true for the language {a^p} p is prine ?

Consider the following decision problems: (P1) Does a given finite state machine accept a given string (P2) Does a given context free grammar generate an infinite number of stings Which of the following statements is true?

Let L denotes the language generated by the grammar S - OSO/00. Which of the following is true?

The number of strings of length 4 that are generated by the regular expression (0+1+|2+3+)*, where | is an alternation character and {+, *} are quantification characters, is:

Consider the CFG with {S,A,B) as the non-terminal alphabet, {a,b) as the terminal alphabet, S as the start symbol and the following set of production rules S --> aB S --> bA B --> b A --> a B --> bS A --> aS B --> aBB A --> bAA Which of the following strings is generated by the grammar?

Formal Languages and Automata Theory: Part A

Compiler Construction and Parsing Algorithms

Compilation and Programming Languages

Filters

Let S and T be language over ={a,b} represented by the regular expressions (a+b) and (a+b)*, respectively. Which of the following is true?

Consider the following two statements: S₁: { 0^2n |n >= l} is a regu1ar language S₂: { 0^m 0^n 0^(m+n) l m >= 1 and n >= 2} is a regu1ar language Which of the following statements is correct?

Consider the following identities for regular expressions: (a) (r + s)* = (s + r)* (b) (r) = r* (c) (r* s) = (r + s)* Which of the above identities are true?

Consider the following decision problems: (P₁) Does a given finite state machine accept a given string (P₂) Does a given context free grammar generate an infinite number of stings Which of the following statements is true?

The number of strings of length 4 that are generated by the regular expression (0+1+|2+3+), where | is an alternation character and {+, } are quantification characters, is: