Theory of Automata (CS402)
Assignment # 2
Solution
Total marks = 20
Deadline Date = Expired
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Question No. 1 [5+5]
Construct deterministic Finite State Automata for each of the following over Σ = {x, y}:
a. Language of all those strings in which second last symbol is ‘y’.
Solution:
b. Language of all those strings whose length is odd and number of y’s is even.
Solution:
Question No. 2 [5+5]
a. Convert the given transition graph (TG) into generalized transition graph (GTG) and derive its regular expression.
Solution:
First of all single initial and single final states are required as given below:
After eliminating state 3 the TG will look like:
Now eliminate state 4
Eliminate state 5
Now eliminate state 6
After eliminating states 1 and 2 the GTG will look like:
b. Find out the union of the given two FAs:
Solution:
| | New states after reading | |
| Old States | | |
| | a | b |
| | | |
| z1 - = (x1, y1) | (x2, y2) = z2 | (x2, y2) = z2 |
| z2= (x2, y2) | (x2, y3) = z3 | (x3, y2) = z4 |
| z3+ = (x2, y3) | (x2, y3) = z3 | (x3, y3) = z5 |
| z4+ =(x3, y2) | (x3, y3) = z5 | (x3, y2) = z4 |
| z5+ = (x3, y3) | (x3, y3) = z5 | (x3, y3) = z5 |
The resultant FA of the union of above two FAs is given below:
