Question 1

The following grammar
G = (N, T, P, S)
N = {S, A, B, C}
T = {a, b, c}
P : S ? aS
A ? bB
B ? cC
C ? a is

Accepted Answer

A)  is type 3
B)  is type 2 but not type 3
C)  is type 1 but not type 2
D)  is type 0 but not type 1 A

Question 2

If G is a connected planar graph of v vertices e edges and r regions then

Accepted Answer

A)  v-e+r=2
B)  e-v+r=2
C)  v+e-r=2
D)  None of above. A

Question 3

Any given transition graph has an equivalent:

Accepted Answer

A)  regular
B)  DFSM (Deterministic Finite State Machine) 
C)  NDFSM
D)  All of them D

Question 4

Given an arbitrary non-deterministic finite automaton NFA with N states, the maximum number of states in an equivalent minimized DFA is at least:

Accepted Answer

A)  N2
B)  2N
C)  2N
D)  N!

Question 5

Which one of the following statement is FALSE?

Accepted Answer

A)  context-free languages are closed under union
B)  context-free languages are closed under concatenation
C)  context-free languages are closed under intersection
D)  context-free languages are closed under Kleene closure

Question 6

Grammars that can be translated to DFAs:

Accepted Answer

A)  Left linear grammar
B)  Right linear grammar
C)  Generic grammar
D)  All of these

Question 7

Which of the following is true with respect to Kleene's theorem?
1 A regular language is accepted by a finite automaton.
2 Every language is accepted by a finite automaton or a turingmachine.

Accepted Answer

A)  1 only
B)  2 only
C)  Both 1 and 2 are true statements
D)  None is true

Question 8

A language L is accepted by a FSA iff it is

Accepted Answer

A)  CFL
B)  CSL
C)  Recursive
D)  Regular

Question 9

Type-1 Grammar is known as_____________

Accepted Answer

A)  CFG
B)  CSG
C)  REGULAR
D)  All

Question 10

Let L1 = {w ? {0,1}? | w has at least as many occurrences of (110)'s as (011)'s}. Let L2 = { ? {0,1}? | w has at least as many occurrences of (000)'s as (111)'s}. Which one of the following is TRUE?

Accepted Answer

A)   L1 is regular but not L2
B)  L2 is regular but not L1
C)  Both L1 and L2 are regular
D)  Neither L1 nor L2 are regular

Question 11

Regular expressions are

Accepted Answer

A)  Type 0 language
B)  Type 1 language
C)  Type 2 language
D)  Type 3 language

Question 12

Let w be any string of length n is {0,1}*. Let L be the set of all substrings of w. What is the minimum number of states in a non-deterministic finite automaton that accepts L?

Accepted Answer

A)  n-1
B)  n
C)  n+1
D)  2n-1

Question 13

Consider the regular language L = (111+111111)*. The minimum number of states inany DFA accepting this language is

Accepted Answer

A)  3
B)  5
C)  8
D)  9

Question 14

Which of the following is TRUE?

Accepted Answer

A)  Every subset of a regular set is regular
B)  Every finite subset of a non-regular set is regular
C)  The union of two non-regular sets is not regular
D)  Infinite union of finite sets is regular

Question 15

Consider the following language L = {anbncndn n ? 1} L is

Accepted Answer

A)  CFL but not regular
B)  CSL but not CFL
C)  Regular
D)  Type 0 language but not type 1

Question 16

If G is a simple connected 3-regular planar graph where every region is bounded by exactly 3 edges, then the edges of G is

Accepted Answer

A)  3
B)  4
C)  6
D)  5

Question 17

A spanning tree for a simple graph of order 24 has

Accepted Answer

A)  12 edges
B)  6 edges
C)  23 edges
D)  None of above.

Question 18

If G is a simple connected 3-regular planar graph where every region is bounded by exactly 3 edges, then the edges of G is

Accepted Answer

A)  3
B)  4
C)  6
D)  5

Question 19

The following grammar
G = (N, T, P, S)
N = {S, A, B, C, D, E}
T = {a, b, c}
P : S ? aAB
AB ? CD
CD ? CE
C ? aC
C ? b
BE ? bc is

Accepted Answer

A)  is type 3
B)  is type 2 but not type 3
C)  is type 1 but not type 2
D)  is type 0 but not type 1

Question 20

Two strings x and y are indistinguishable if:

Accepted Answer

A)  ?*(s, x)  = ?* (s, y) , i.e. the state reached by a DFA M on input x is the same as the state reached by M on input y
B)  if for every string z ? ?* either both xz and yz are in language A on ?* or both xz and yz are not in A
C)  Both above statements are true
D)  None of the above

Exam 1: Formal Languages and Automata Theory: Part A

The following grammar G = (N, T, P, S) N = {S, A, B, C} T = {a, b, c} P : S ? aS A ? bB B ? cC C ? a is

If G is a connected planar graph of v vertices e edges and r regions then

Any given transition graph has an equivalent:

Given an arbitrary non-deterministic finite automaton NFA with N states, the maximum number of states in an equivalent minimized DFA is at least:

Which one of the following statement is FALSE?

Grammars that can be translated to DFAs:

Which of the following is true with respect to Kleene's theorem? 1 A regular language is accepted by a finite automaton. 2 Every language is accepted by a finite automaton or a turingmachine.

A language L is accepted by a FSA iff it is

Type-1 Grammar is known as_____________

Let L₁ = {w ? {0,1}? | w has at least as many occurrences of (110) 's as (011) 's}. Let L₂ = { ? {0,1}? | w has at least as many occurrences of (000) 's as (111) 's}. Which one of the following is TRUE?

Regular expressions are

Let w be any string of length n is {0,1}*. Let L be the set of all substrings of w. What is the minimum number of states in a non-deterministic finite automaton that accepts L?

Consider the regular language L = (111+111111) *. The minimum number of states inany DFA accepting this language is

Which of the following is TRUE?

Consider the following language L = {anbncndn n ? 1} L is

If G is a simple connected 3-regular planar graph where every region is bounded by exactly 3 edges, then the edges of G is

A spanning tree for a simple graph of order 24 has

If G is a simple connected 3-regular planar graph where every region is bounded by exactly 3 edges, then the edges of G is

The following grammar G = (N, T, P, S) N = {S, A, B, C, D, E} T = {a, b, c} P : S ? aAB AB ? CD CD ? CE C ? aC C ? b BE ? bc is

Two strings x and y are indistinguishable if:

Exam 1: Formal Languages and Automata Theory: Part A

The following grammar G = (N, T, P, S) N = {S, A, B, C} T = {a, b, c} P : S ? aS A ? bB B ? cC C ? a is

If G is a connected planar graph of v vertices e edges and r regions then

Any given transition graph has an equivalent:

Given an arbitrary non-deterministic finite automaton NFA with N states, the maximum number of states in an equivalent minimized DFA is at least:

Which one of the following statement is FALSE?

Grammars that can be translated to DFAs:

Which of the following is true with respect to Kleene's theorem? 1 A regular language is accepted by a finite automaton. 2 Every language is accepted by a finite automaton or a turingmachine.

A language L is accepted by a FSA iff it is

Type-1 Grammar is known as_____________

Let L1 = {w ? {0,1}? | w has at least as many occurrences of (110) 's as (011) 's}. Let L2 = { ? {0,1}? | w has at least as many occurrences of (000) 's as (111) 's}. Which one of the following is TRUE?

Regular expressions are

Let w be any string of length n is {0,1}*. Let L be the set of all substrings of w. What is the minimum number of states in a non-deterministic finite automaton that accepts L?

Consider the regular language L = (111+111111) *. The minimum number of states inany DFA accepting this language is

Which of the following is TRUE?

Consider the following language L = {anbncndn n ? 1} L is

If G is a simple connected 3-regular planar graph where every region is bounded by exactly 3 edges, then the edges of G is

A spanning tree for a simple graph of order 24 has

If G is a simple connected 3-regular planar graph where every region is bounded by exactly 3 edges, then the edges of G is

The following grammar G = (N, T, P, S) N = {S, A, B, C, D, E} T = {a, b, c} P : S ? aAB AB ? CD CD ? CE C ? aC C ? b BE ? bc is

Two strings x and y are indistinguishable if:

Let L₁ = {w ? {0,1}? | w has at least as many occurrences of (110) 's as (011) 's}. Let L₂ = { ? {0,1}? | w has at least as many occurrences of (000) 's as (111) 's}. Which one of the following is TRUE?