Question

Let M = ({q0, q1, q2, q3, q4, q5}, {a, b, n}, q0, fs, {q2, q3, q4}) be the Deterministic Finite Automaton (DFA) with state transition function, fs defined as follows: f(q0, a) = q1 f(q0, b) = q0 f(q0, n) = q2 f(q1, a) = q2 f(q1, b) = q1 f(q1, n) = q1 f(q2, a) = q3 f(q2, b) = q2 f(q2, n) = q4 f(q3, a) = q1 f(q3, b) = q3 f(q3, n) = q4 f(q4, a) = q3 f(q4, b) = q5 f(q4, n) = q5 f(q5, a) = q4 f(q5, b) = q3 f(q5, n) = q5 c) Is the input string banana accepted by the DFA? Justify your answer. (2 marks) d) Find ONE input strings that follow the given conditions and must accepted by machine M. (6 marks) i. Length of strings is 4 and do not contains input n. ii. Length of strings is 5 and do not contains input b. iii. Length of strings is 3, start and end with the same input string (for example: aba). You must show the sequence of state transition in each question.

          Let M = ({q0, q1, q2, q3, q4, q5}, {a, b, n}, q0, fs, {q2, q3, q4}) be the Deterministic Finite Automaton (DFA) with state transition function, fs defined as follows:
f(q0, a) = q1 f(q0, b) = q0 f(q0, n) = q2
f(q1, a) = q2 f(q1, b) = q1 f(q1, n) = q1
f(q2, a) = q3 f(q2, b) = q2 f(q2, n) = q4
f(q3, a) = q1 f(q3, b) = q3 f(q3, n) = q4
f(q4, a) = q3 f(q4, b) = q5 f(q4, n) = q5
f(q5, a) = q4 f(q5, b) = q3 f(q5, n) = q5
c) Is the input string banana accepted by the DFA? Justify your answer. (2 marks)
d) Find ONE input strings that follow the given conditions and must accepted by machine M. (6 marks)
i. Length of strings is 4 and do not contains input n.
ii. Length of strings is 5 and do not contains input b.
iii. Length of strings is 3, start and end with the same input string (for example: aba).
You must show the sequence of state transition in each question.

Show more…

Let M = (q0, q1, q2, q3, q4, q5, a, b, n, q0, fs, q2, q3, q4) be the Deterministic Finite Automaton (DFA) with state transition function, fs defined as follows:
f(q0, a) = q1 f(q0, b) = q0 f(q0, n) = q2
f(q1, a) = q2 f(q1, b) = q1 f(q1, n) = q1
f(q2, a) = q3 f(q2, b) = q2 f(q2, n) = q4
f(q3, a) = q1 f(q3, b) = q3 f(q3, n) = q4
f(q4, a) = q3 f(q4, b) = q5 f(q4, n) = q5
f(q5, a) = q4 f(q5, b) = q3 f(q5, n) = q5
c) Is the input string banana accepted by the DFA? Justify your answer. (2 marks)
d) Find ONE input strings that follow the given conditions and must accepted by machine M. (6 marks)
i. Length of strings is 4 and do not contains input n.
ii. Length of strings is 5 and do not contains input b.
iii. Length of strings is 3, start and end with the same input string (for example: aba).
You must show the sequence of state transition in each question.

Added by Diana A.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Sri K

04/20/2023

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First, let's rewrite the given state transition function in a more readable format: Show more…

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Let M = ({q0, q1, q2, q3, q4, q5}, {a, b, n}, q0, fs, {q2, q3, q4}) be the Deterministic Finite Automaton (DFA) with state transition function, fs defined as follows: f(q0, a) = q1 f(q0, b) = q0 f(q0, n) = q2 f(q1, a) = q2 f(q1, b) = q1 f(q1, n) = q1 f(q2, a) = q3 f(q2, b) = q2 f(q2, n) = q4 f(q3, a) = q1 f(q3, b) = q3 f(q3, n) = q4 f(q4, a) = q3 f(q4, b) = q5 f(q4, n) = q5 f(q5, a) = q4 f(q5, b) = q3 f(q5, n) = q5

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