#FiniteAutomatappt

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Construct The Minimal Finite Automata That Accept All The String Of a & b Such That There Is Even No. Of a And Even Number Of b

Construct The Minimal Finite Automata That Accept All The String Of a & b Such That i) There Is Even No. Of a And Even Number Of b   Solution:- Question Is Final Automata Should Contain Even Number Of 'a's And Even Number Of 'b's Even Numbers Are 0,2,4,6,8,.....  

CREATE TWO SEPARATE AUTOMATAS WITH GIVEN TWO CONDITIONS

Finite Automata 1:- Even Number Of 'a's Σ={a,b}

q0 Is My Initial And Final State Because Of ε q0 Goes To q1 And q1 Goes To q0(aa) I Dont Bother About Number Of b's On q0q1 Finite Automata 2:- Even Number Of b's(ε,bb,bbbb,bbbbbb....)

I Have Drawn Finite Automata 2 Using The Same Procedure Used In Finite Automata 1.   Now Cross Product (Or) Cross Multiplication Finite Automata 1 × Finite Automata 2

=> {(q0,q2),(q0,q3) (q1,q2),(q1,q3)}  NOS - 4   Now DRAW FINAL DFA Using These States By Observing Finite Automata 1 And Finite Automata 2

Final State Will Be The Combination Of Finite Automata 1 And Finite Automata 2 Only. Because The Condition Given Is Two Conditions Should Be Satisfied. No Of Even 'a's And No. Of Even b's In A String.   Cross Check abaaba

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Construct Minimal Deterministic Finite Automata (DFA) Start And End With Different Symbol

Construct Minimal Deterministic Finite Automata (DFA) Start And End With Different Symbol Where Σ={a,b}   Condition Given Is If Your String Is Starting With 'a' It Should End With 'b' If Your String Is Starting With 'b' Then It Should End With 'a'   L={ab,ba,abbb,abab,baba,bbaa.........} // Infinite Language

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