Assignment 2
1. Write down the definition of Regular Language with suitable example.
2. Determine the following claims are true or false for all regular expressions ๐1 and ๐2. The symbol
โก stands for equivalence.
a. (๐1
โ)โโก ๐1
โ
b. (๐1
โ๐2
โ)โโก (๐1+ ๐2)โ
c. (๐1
โ๐2
โ)โโก(๐1๐2)โ
3. Give the regular expression of following languages with ฮฃ = {๐, ๐}:
a. ๐ฟ1= {๐๐๐๐|๐ โค 4 ๐๐๐ ๐ โฅ 1}
b. ๐ฟ2= {๐๐๐๐|(๐ + ๐) ๐๐ ๐๐๐}
c. ๐ฟ3= {๐๐๐๐|๐ โฅ 3 ๐๐๐ ๐ ๐๐ ๐๐ฃ๐๐}
d. ๐ฟ1
๏ค
๏ค
๏ค
e. ๐ฟ2
๏ค
๏ค
๏ค
f. ๐ฟ3
๏ค
๏ค
๏ค
g. ๐ฟ4= {๐ฃ๐ค๐ฃ|๐ฃ, ๐ค๐{๐ , ๐}โ ๐๐๐ |๐ฃ|โค 2}
h. ๐ฟ5= {๐ค|๐ค๐{๐, ๐ }โ ๐๐๐ |๐ค|๐๐๐3 = 0}
i. ๐ฟ5
๏ค
๏ค
๏ค
4. Give the regular expression of the following languages with ฮฃ = {๐, ๐, ๐}:
a. All strings having exactly two aโs.
b. All strings having at least two aโs.
c. All strings having at most two aโs.
d. All strings having at least one occurrence of each alphabet.
e. All strings in which all runs of aโs lengths that are multiples of three.
5. Give the regular expression of following languages with ฮฃ = {0, 1}:
a. All strings ending with 11.
b. All strings not ending with 11.
c. All strings, in which first two and last two symbols are same and the length of string is
more than 3.
d. All strings with even number of 1โs.
e. All strings having two times occurrence of 00. 000 is also counted as two time
occurrence of 00.
6. Construct the Generalized Transition Graph (GTG) and find the regular expression of the
following languages:
a. ๐ฟ = {๐ค๐{0,1}โ|๐๐ข๐๐๐๐ ๐๐(0)= 2๐ + 1 ๐๐๐ ๐๐ข๐๐๐๐ ๐๐(1)= 2๐ + 1 ๐คโ๐๐๐ ๐, ๐ โฅ
0}
b. ๐ฟ = {๐ค๐{0,1}โ|๐๐ข๐๐๐๐ ๐๐(0)= 2๐ ๐๐๐ ๐๐ข๐๐๐๐ ๐๐(1)= 2๐ ๐คโ๐๐๐ ๐, ๐ โฅ 0}
7. Proof that if ๐ฟ is a regular language then there exist a regular expression ๐ such that ๐ฟ = ๐ฟ(๐).
8. Construct the NFA that accepts the following languages on alphabets ฮฃ = {๐, ๐ }:
a. ๐ฟ(๐โ+ ๐โ(๐ + ๐)๐โ)
b. ๐ฟ(๐๐โ๐๐ +๐๐๐โ๐๐)
c. ๐ฟ((๐๐๐๐)โ+ (๐๐๐โ+ ๐)โ)
