![Consider the finite automaton M = (Q,{a, b},8,90,F) defined by the following illustration. -0.00 7 92 Part (a) (8 MARKS] For](http://img.homeworklib.com/questions/56d39a60-cf01-11eb-ac21-adca92598bf6.png?x-oss-process=image/resize,w_560)
Homework Answers
From starting state q0 , the last state will be q0 only if there is repeated sequence of ab so that on input a, transition from q0 to q1 will happen and from input b, transition from q1 to q0 will happen.
Hence, regular expression R0 for the given DFA such
that last state should be q0 is given by R0 =
(ab)* which means any possible repetition of sequence ab. Hence
State q1 is reached, only when previous state was
q0 and input a is supplied. Hence regular expression for
R1 can be obtained from regular expression for
R0 by inserting a at the end. Hence regular expression
for R1 = (ab)*a i.e.
State q2 is reached either when input b is given to state q0 or input b is given to state q3 . State q3 is reached when either input a is given to q1 or input a is given to q2 .
Regular expression for q2 is R2 = (ab)*b + (ab)*aa(ba)*b .
Here, (ab)*b is the path to reach q2 from q0 and (ab)*aa(ba)*b is the path to reach q2 from q0 to q1 then from q1 to q3 and then q3 to q2 .
Regular expression for q3 is R3 = b(ab)*a + (ab)*aa(ba)*
Please comment for any clarification.
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Consider the finite automaton M = (Q,{a, b},8,90,F) defined by the following illustration. -0.00 7 92...
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Exercise 41.2 Consider the signal f(t) window w(t)e amat, α E R, and the Gaussian (a) Verify that is well-defined (even though f f L'(R)). (b) Compute Ws(A, b) using the following result: e-ra(1+iz)2 dt = a-2 For a > 0 and E R, (c) Show that l W, (A, b)12 attains its maximum when λ a.
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