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### Conversion Of E-NFA To NFA – Finite Automata –

Conversion Of E-NFA To NFA - Finite Automata The Process Of Conversion Of ε-NFA To NFA Is Called As Thomson Construction. Note:- No Change In Initial State No Change In The Total No. Of States May Be Change In Final States Algorithm Let M=(Q,Σ,δ,q0,F) - ε-NFA M1= (Q1,Σ,δ1,q01,F1) - NFA 1) Initial State q01=q0 2) Construction Of δ1 δ1 (q,x)=ε-Closure(δ(ε-Closure(q),x) 3) Final State Every State Who's ε-Closure

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### DFA Example : Complement Of Finite Automata

Complement Of Finite Automata Means The Finite Automata Which Is Obtained By Interchanging Final And Non-Final States Is Known As Complement Of Finite Automata. In This Concept, I'll Change Final States To Non-Final To Final State And Final To Non-Final State. By Doing This The Language Changes. M-Automata(DFA) L-Language M Supports L Language   The String Which

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### Compound Automata (DFA Example): 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

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### Compound Automata (DFA Example): 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

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### Compound Automata(DFA Example): Construct The Minimal Finite Automata That Accept All The String Of a & b Such That There Is One ‘a’ Or One ‘b’

Construct The Minimal Finite Automata That Accept All The String Of a & b Such That i) There Is One 'a' Or One 'b'   Solution:- Compound Automata Means Combining Two Automata's (Machines) Which Becomes One Automata(Machine). Let's Know Why We Should Combine Two Automata. If The Question Contains More Than One Condition ' I Have Solved

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### Construct The Minimal Finite Automata And Find The Number Of States In Following Language

Construct The Minimal Finite Automata And Find The Number Of States In Following Language L={ambn/m≥0,n≥2018}   This Is A Interesting Problem. Given m≥0 n≥2018 // 2018 Is A Big Number, It Becomes Very Big DFA But We Need Minimal DFA. Σ={a,b} m≥0 Let n≥1 So My Language Is L={b,bb,bbb,bbbb.......} // ε Epsilon Is Not There Because m=0,n=0,n=1 means 'b'   i)   ii) m≥0,n≥2 So

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### DFA Example : Construct The Minimal Finite Automata That Accepts All Base 8 Numbers Which Are Divisible By ‘6’

Construct The Minimal Finite Automata That Accepts All Base 8 Numbers Which Are Divisible By '6' (Binary Means Base 2, i.e Σ(0,1) Input Symbols Will Be 2 Only 0 & 1) (Integer Means Base 10,i.e (0,1,2,3,4,5,6,7,8,9) Input Symbols Will Be 10 Only 0&1&2&3&4&5&6&7&8&9)   Here Given Input Symbols Are Base '8', It Means OCTAT. My Input

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### DFA Example : Construct Minimal Finite Automata That Accepts All Strings Of 0’s & 1’s Such That a) |w|≅0 (mod 2), b) |w|≅1 (mod 2), c) |w|≅2 (mod 3)

Construct Minimal Finite Automata That Accepts All Strings Of 0's & 1's Such That a) |w|≅0 (mod 2), b) |w|≅1 (mod 2), c) |w|≅2 (mod 3) |w|= Length Of 'w' String a) |w|≅0 (mod 2) Means If I Divide Length Of String With '2' I Should Get Remainder '1' 'ε' Is Length '0' String,

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### Construct Minimal Finite Automata That Accepts All Strings Of 0’s And 1’s Such That i) η0|w|≅0 (mod 3) ii) η0|w|≅0 (mod 4)

Construct Minimal FA That Accepts All Strings Of 0's And 1's Such That i) η0|w|≅0 (mod 3) ii) η0|w|≅0 (mod 4) Σ={0,1} i) η0|w|≅0 (mod 3) // η0 Is No. Of Zero's, |w| Is In The String, If I Divide With '3', I'll Get Remainder '0'. Means, The No. Of 0's In The String,If I Divide

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### DFA Example : Construct Minimal Finite Automata That Accept All The Strings Of 0’s And 1’s Such That Exactly Two 0’s

Construct Minimal Finite Automata That Accept All The Strings Of 0's And 1's Such That i) Exactly Two 0's ii) Almost Two 0's iii) Atleast Two 0's   Solution There Σ={0,1} // Here In The Place Of a,b The Input Alphabets Are a,b   i) Exactly Two 0's Possible Strings :- {00,001,01011,100,1001....} // String Should Contain Exactly Two 0's Small String Is 00 Here

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