DFA assignment solution by Kamran zafar Class BSCS(E)A in university of okara and madam is Amna

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Example: Consider the language L of strings, defined
over Σ={a, b}, starting with b. The language L may
be expressed by RE b(a + b)*
, may be accepted by the
following FA
a,b
a,b
b
a
–– +
1
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 Example:
Consider the language L of strings, defined over
Σ={a, b}, ending in a. The language L may be
expressed by RE
(a+b)*
a
This language may be accepted by the following FA
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Example Continued …
There may be another FA corresponding to the given
language.
a
b
+
b
–
a
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Example continued …
a
b
b
b
a
+
a
––
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Note
 It may be noted that corresponding to a given language
there may be more than one FA accepting that
language, but for a given FA there is a unique language
accepted by that FA.
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Note
 It is to be noted that given the languages L1 and L2
,where
L1 = The language of strings, defined over Σ={a, b},
beginning with a
L2 = The language of strings, defined over
Σ={a, b}, not beginning with b
The  does not belong to L1 while it does belong to L2 .
This fact may be depicted by the corresponding
transition diagrams of L1 and L2.
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FA1
Corresponding to L1
 The language L1
may be expressed by the regular
expression a(a + b)*
a,b
a
b a,b
–– +
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FA2
Corresponding to L2
 The language L2
may be expressed by the regular
expression a (a + b)*
+ Λ
a,b
a,b
a
b
 +
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Example
 Consider the Language L of Strings of length two or
more, defined over Σ = {a, b}, beginning with and
ending in same letters.
The language L may be expressed by the following
regular expression
a (a + b)*
a + b (a + b)*
b
It is to be noted that if the condition on the length of
string is not imposed in the above language then the
strings a and b will then belong to the language.
This language L may be accepted by the following FA
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Example Continued …
b
a
a
b
+
a
b
b
a
+
b
a
–
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Task
 Build an FA accepting the Language L of Strings,
defined over Σ = {a, b}, beginning with and ending
in same letters.
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Example
Consider the language L = {w belongs to {a,b}*
:
length(w) >= 2 and w neither ends in aa nor bb}.
The language L may be expressed by the regular
expression
(a+b)*
(ab+ba)
This language may be accepted by the following FA
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Example Continued …
b
a
b
4+
b
2
a
a
5+
a
3
b
1–
a b
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Note
 It is to be noted that building an FA corresponding to
the language L, discussed in the previous example,
seems to be quite difficult, but the same can be done
using tree structure along with the technique
discussed in the book
Introduction to Languages and Theory of
Computation, by J. C. Martin
so that the strings ending in aa, ab, ba and bb should
end in the states labeled as aa, ab, ba and bb,
respectively;as shown in the following FA
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Example continued …
a
a
aa
b
a
b
Λ
a
b
a
a
a
b
b
b
b
a
b
ab
ba
bb
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Task
 Using the technique discussed by Martin, build an FA
accepting the following language
L = {w belongs to {a,b}*
: length(w) >= 2 and second
letter of w, from right is a}.
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Task
 Using the technique discussed by Martin, build an FA
accepting the following language
L = {w belongs to {a,b}: w neither ends in ab nor ba}.
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37. Thanks....
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