#finiteautomataunionexample

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Construct The Minimum Finite Automata That Accept All The Strings Of a & b Such That String Contains At least 2 a's & ηb|w|≅0mod3

Construct The Minimum Finite Automata That Accept All The Strings Of a & b Such That

i) String Contains At least 2 a's & ηb|w|≅0mod3

Solution:- (Check Previous Two Problems For Better Understanding) CONDITION GIVEN:- String Should Contain At least 2 a's And ηb|w|≅0mod3(Means No Of b's In String Is Approximately Equal To O Mod 3(If I Divide The No.Of b's With 3, I Should Get Remainder As 0)  

FINITE Automata 1:-

Σ={a,b} L={aa,aaa,aaaa,aaaaa....}

FINITE AUTOMATA 2:-

ηb|w|≅0mod3 Means No Of b's In String Is Approximately Equal To O Mod 3(If I Divide The No.Of b's With 3, I Should Get Remainder As 0

Possible Remainders For 3 Are 0,1,2   Mean If I Divide No. Of b's In A String With 3 I Should Get Remainder As 0   Imagine-{b,bbb,babbab,bbabbbbba....} If No Of b's Are '0' In A String And If I Divide 3 With 0 I'll Get Remainder '0'   0 Is Divisible By 3 0 Means ε Means L={ε,1,2,3}={ε,b,bb,bbbb...}

CROSS PRODUCT FINITE AUTOMATA 1 × FINITE AUTOMATA 2 => {(q0,q3),(q0,q4),(q0,q5), (q1,q3),(q1,q4),(q1,q5), (q2,q3),(q2,q4),(q2,q5)}  

FINITE AUTOMATA

FINAL STATE Is q2,q3  Because Two Conditions Should Satisfy. CROSS CHECK babab // aa,bbb Read the full article