Question 1

Let L = L1 \cap L2, where L1 and L2 are languages as defined below: L1 = {a^{m}b^{m}ca^{n}b^{n} | m, n >= 0 } L2 = {a^{i}b^{j}c^{k} | i, j, k >= 0 } Then L is

Accepted Answer

A) Not recursive 
B) Regular 
C) Context free but not regular 
D) Recursively enumerable but not context free.

Question 2

Consider the following Finite State Automaton The language accepted by this automaton is given by the regular expression

Accepted Answer

A) b*ab*ab*ab 
B) (a+b)* 
C) b*a(a+b)* 
D) b*ab*ab

Question 3

Let L={w \in (0 + 1)*|w has even number of 1s}, i.e. L is the set of all bit strings with even number of 1s. Which one of the regular expression below represents L?

Accepted Answer

A) (0*10*1)* 
B) 0*(10*10*)* 
C) 0*(10*1*)*0* 
D) 0*1(10*1)*10*

Question 4

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 5

The language L = { 0^i 2 1 ^i i>-0 } over the alphabet (0,1,2) is

Accepted Answer

A) not recurcise 
B) is recursive and deterministic CFL 
C) is a regular language 
D) is not a deterministic CFL but a CFL

Exam 1: Formal Languages and Automata Theory: Part A

Let L = L₁ \cap L₂, where L₁ and L₂ are languages as defined below: L₁ = {a^{m}b^{m}ca^{n}b^{n} | m, n >= 0 } L₂ = {a^{i}b^{j}c^{k} | i, j, k >= 0 } Then L is

Consider the following Finite State Automaton The language accepted by this automaton is given by the regular expression

Let L={w \in (0 + 1) *|w has even number of 1s}, i.e. L is the set of all bit strings with even number of 1s. Which one of the regular expression below represents L?

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?

The language L = { 0^i 2 1 ^i i>-0 } over the alphabet (0,1,2) is