CS402 - Theory of Automata Assignment No.1 Semester: Fall 2019
Assignment No. 01Semester: Fall 2019Theory of Automata – CS402
Objectives:
Objective
of this assignment is to assess the understanding of students about the concept
of languages, regular expressions and finite automata.
Instructions:
Please
read the following instructions carefully before submitting assignment:
•
You should consult the recommended books, PowerPoint slides
and audio lectures to clarify your concepts.
•
You are supposed to submit your assignment in .doc format. Any other formats like
scan images, PDF, zip, rar and bmp etc will not be accepted.
•
It should be clear that your assignment will not
get any credit if:
•
The assignment is submitted after due date.
•
The assignment is copied from Internet or from any
other student.
•
The submitted assignment does not open or file is
corrupt.
Note: No assignment will be accepted after the due date through
email in any case (load shedding, server down, internet malfunctioning etc.).
It is recommended to upload solution
file at least two days before its closing date.
Question:
Marks= 20
Q1. Show
that the following pairs of regular expressions define the same language over
the alphabet
L =
{a, b}.
(i) (ab)*a
and a(ba)*
(ii) (a* + b)*
and (a + b)*
(iii) (a* + b*)* and
(a + b)*
•
Since the strings generated by
language (ab)*a and a(ba)* define the same strings ending in a hence both
RE define the same language.
•
Both RE define the same language of
all string containing any number of a’s and b’s
•
Since (a* + b*)* and (a + b)*
generate all string containing any number of a’s and b’s hence both RE
define the same language.
[9 marks = 3*3]
Answer:-
1. 1. Since the strings generated by language (ab)*a and a(ba)* define the same strings ending in a hence both RE define the same language.
2.
Both RE
define the same language of all string containing any number of a’s and b’s3.
Since (a*
+ b*)* and (a + b)* generate all string containing any number of a’s and
b’s hence both RE define the same language.
Question no 2:-
Develop a regular expression for the following language over the alphabet P =
{a, b} such that it accepts all strings in which the letter b is never tripled.
This means that no word contains the substring bbb.
[5 marks]
(Λ + b + bb)(a + ab
+ abb)*
Since we need to define RE for a language that have strings like {Λ,
abb,abba, aabbaa,…}
Hence the RE for this language would be (a * +
bb)*
Answer:-
Since we need to define RE for a language that have strings like {Λ, abb,abba, aabbaa,…}HenceThe RE for this language would be (a * + bb)*
Question no 3:-
.
Develop a regular expression for the following language over the alphabet P =
{a, b} such that it accepts all strings all words in which a is tripled or b is
tripled, but not both. This means each word contains the substring aaa or the
substring bbb but not both. [ 6 marks]
((Λ + b + bb)(a
+ ab + abb)*aaa(Λ + b + bb)(a + ab + abb)*)+ ((Λ + a + aa)(b + ba + baa)*bbb(Λ
+ a + aa)(b + ba + baa)*)
Since we need to develop a RE for a
language that have strings like {aaab, bbbaa, aaabb}
Hence the required RE for this language
would be (aaa+ + b) + (bbb+ + a)
