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Give a DFA for Σ = {a, b} that accepts strings with {a^nbb: n>=0} U {b^naa: n>=1}
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DFA (Theory of Computation)
1.
2.
Faysal Ahmad 15203033 Abdullah
Al Shakil 15203058 Susmita Banik 15203099 Sharmin Zahan 15203105 Theory of Computation CSC 397 Sec-G 2IUBAT
3.
3 Automata Finite Automata Push Down Automata DFANFA Turing Machine IUBAT
4.
Problem: Pluto Give a
DFA for Σ = {a, b} that accepts strings with {a^nbb: n>=0} U {b^naa: n>=1} 4IUBAT
5.
Problem Definition Alphabet: Σ
= { a. b } L(M)={w|w {a^nbb: n>=0} U {b^naa: n>=1} } L(M)={bb, abb, aabb…} U {baa, bbaa, bbbaa… } L(M)={bb, abb, aabb, baa, bbaa, bbbaa… } 5IUBAT
6.
Formal Definition •Components of
FSM are 5 tuples {Q, ∑, δ, q0, F} •Q = {q0, q1, q2, q3, q4, q5, q6, q7, q8, q9} •∑ = {a, b} •δ = (q1, b) = q2 •q0 = q0 •F = q5, q7, q8 6IUBAT
7.
Present State a b q0 q1
q4 q1 q1 q2 q2 q9 q3 q3 q9 q9 q4 q7 q5 q5 q7 q6 q6 q7 q6 q7 q8 q9 q8 q9 q9 q9 q9 q9 Transition Table 7IUBAT
8.
q0 q1 a a q2 b a q3 b q3 q4 b q5 b q6 a a a q7 q8 a q8 q9 b a,b a,b a,b b b 8IUBAT
9.
q0 q1 a a q2 b q3 b q3 q4 b q5 b q6 a a a q7
q8 a q8 q9 b a,b a,b a,b b b 9 a b b a IUBAT
10.
q0 q1 a a q2 b q3 b q3 q4 b q5 b q6 a a a q7
q8 a q8 q9 b a,b a,b a,b b b 10 a b b a IUBAT
11.
q0 q1 a a q2 b q3 b q3 q4 b q5 b q6 a a a q7 q8 a q8 q9 b a,b a,b a,b a b b b b 11 a IUBAT
12.
q0 q1 a a q2 b q3 b q3 q4 b q5 b q6 a a a q7 q8 a q8 q9 b a,b a,b a,b a b b b b 12 a IUBAT
13.
q0 q1 a a q2 b q3 b q3 q4 b q5 b q6 a a a q7 q8 a q8 q9 b a,b a,b a,b a b b b b 13 Accepted a IUBAT
14.
q0 q1 a a q2 b q3 b q3 q4 b q5 b q6 a a a q7 q8 a q8 q9 b a,b a,b a,b b b b b 14 Accepted a IUBAT
15.
q0 q1 a a q2 b q3 b q3 q4 b q5 b q6 a a a q7 q8 a q8 q9 b a,b a,b a,b b b b b 15 Accepted a IUBAT
16.
q0 q1 a a q2 b q3 b q3 q4 b q5 b q6 a a a q7 q8 a q8 q9 b a,b a,b a,b b b b b 16 Accepted Accepted a IUBAT
17.
q0 q1 a a q2 b q3 b q3 q4 b q5 b q6 a a a q7
q8 a q8 q9 b a,b a,b a,b b a a b b 17 a IUBAT
18.
q0 q1 a a q2 b q3 b q3 q4 b q5 b q6 a a a q7
q8 a q8 q9 b a,b a,b a,b b a a b b 18 a IUBAT
19.
q0 q1 a a q2 b q3 b q3 q4 b q5 b q6 a a a q7
q8 a q8 q9 b a,b a,b a,b b a a b b 19 a IUBAT
20.
q0 q1 a a q2 b q3 b q3 q4 b q5 b q6 a a a q7
q8 a q8 q9 b a,b a,b a,b b a a b b 20 a IUBAT
21.
q0 q1 a a q2 b q3 b q3 q4 b q5 b q6 a a a q7
q8 a q8 q9 b a,b a,b a,b b b b b b 21 a IUBAT
22.
q0 q1 a a q2 b q3 b q3 q4 b q5 b q6 a a a q7
q8 a q8 q9 b a,b a,b a,b b b b b b 22 a IUBAT
23.
q0 q1 a a q2 b q3 b q3 q4 b q5 b q6 a a a q7
q8 a q8 q9 b a,b a,b a,b b b b b b 23 a IUBAT
24.
q0 q1 a a q2 b q3 b q3 q4 b q5 b q6 a a a q7
q8 a q8 q9 b a,b a,b a,b b b b b b 24 Rejected a IUBAT
25.
q0 q1 a a q2 b q3 b q3 q4 b q5 b q6 a a a q7 q8 a q8 q9 b a,b a,b a,b b b a b b b 25 a IUBAT
26.
q0 q1 a a q2 b q3 b q3 q4 b q5 b q6 a a a q7 q8 a q8 q9 b a,b a,b a,b b b a b b b 26 a IUBAT
27.
q0 q1 a a q2 b q3 b q3 q4 b q5 b q6 a a a q7 q8 a q8 q9 b a,b a,b a,b b b a b b b 27 a IUBAT
28.
q0 q1 a a q2 b q3 b q3 q4 b q5 b q6 a a a q7 q8 a q8 q9 b a,b a,b a,b b b a b b b 28 a IUBAT
29.
q0 q1 a a q2 b q3 b q3 q4 b q5 b q6 a a a q7 q8 a q8 q9 b a,b a,b a,b b b a b b b 29 Rejected a IUBAT
30.
30IUBAT
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