Compiler Design Spring 2010 (CSE344)
Assignment # 1
Date of Submission: 1st March 2010
Instructor : Asma Sanam Larik
Mode of Submission: Hand Written
Question #1:
Construct a Deterministic Finite Automata and write down Regular Expressions
for the following languages:
i.
L={w | na (w)=2 , w Є (a,b)*} where : na (w) means number of a’s in w
ii.
Language over Σ = {a,b} in which every occurrence of a bb is followed by
an a
iii.
Language over Σ = {a,b} that does not contain aaa as a substring
iv.
Language over Σ = {a,b} that accepts all the strings that do not end with ba
v.
The set of all strings beginning with a 1, that interpreted as a binary
number is a multiple of 5. For example the strings 101, 1010 and 1111 are
in the language but 0, 100 and 111 are not
vi.
Language that accepts all the strings over Σ = {a,b} that have both or
neither aa and bb as substrings
vii.
Language of all the strings containing no more than one occurrence of
string 00 over Σ = {0,1} (Note: The string 000 should be viewed as
containing two occurrences of 00)
Question #2:
Describe the language accepted by the following automata:
a)
b)
c)
a b
a b
a
b
p q q
p q q
p
{q}
q
r p
q r s
q
{q} {q,r}
*r
q q
*r q q
*r
s
s
q q
*s
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Compiler Design Spring 2010 (CSE344)
Assignment # 1
Question #3:
Convert the following є-NFA to DFA:
a)
c)
є
a
b
p
{r}
{q}
{r}
 q1
q
{s}
{t}
q2
r
{q}
{t}
q3
*s
*q4
t
{ s,t}
є
{q2,q3}
{q4}
{q2}
a
{q3}
{q3}
Question #4:
Minimize the following DFA (Show all the necessary steps)
q1
q2
q3
q4
*q5
a
q2
q3
q4
q4
q4
b
q1
q1
q5
q5
q5
Question #5:
We can prove that two regular expressions aer equivalent by showing that their
minimum-state DFA’s are same, except for the state names. Using this technique
show that the following reqular expressions are equivalent:
a) (a|b)*
b) (a* |b*) *
c) ((є |a) b*) *
------------------------------------------ Good Luck------------------------------------------
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