Automata theory -Conversion of ε nfa to nfa
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1) An epsilon-NFA (ε-NFA) is converted to a non-deterministic finite automaton (NFA) by taking the epsilon-closure of each state. 2) The initial state and number of states remain the same, but the final states and transitions may change. 3) The procedure takes the epsilon-closure of the source states for each transition and uses it as the target of the corresponding transition in the new NFA.
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Automata theory -Conversion of ε nfa to nfa
- 1. Given: Conversion Of ε-NFA To NFA Note: 1.No Change In Initial State 2.No Change In The Total No. Of States 3.May Be Change In Final States 4. Changes in Transitions
- 2. ε-Closure(q0)={q0,q1} ε-Closure(q1)={q1} • Let NFA –ε be M=(Q,Σ,δ,q0,F) NFA be M1= (Q1,Σ,δ1,q0 1,F1) Initial state of given nfa-ε is {q0} Now, initial state of nfa will be {q0} Now find the transition of q0 on inputs 0,1 δ1=(q0,0)=ε-Closure(δ(ε-Closure(q0),0)) =ε-Closure(δ({q0,q1},0)) =ε-Closure(q0) ={q0,q1} δ1=(q0,1)=ε-Closure(δ(ε-Closure(q1),1)) =ε-Closure(δ({q0,q1},1)) =ε-Closure(q1) ={q1} δ1=(q1,0)=ε-Closure(δ(ε-Closure(q1),0)) =ε-Closure(δ({q1},0)) =ε-Closure(Φ) =Φ δ1=(q1,1)=ε-Closure(δ(ε-Closure(q1)1)) =ε-Closure(δ({q1},1)) =ε-Closure(q1) ={q1}
- 3. Resultant NFA is input State 0 1 *q0 {q0,q1} {q1} * q1 Φ {q1} Final State? q0 & q1 Both are final states because ε-Closure(q0)={q0,q1} ε-Closure(q1)={q1} NFA - Transition diagram NFA - Transition table
- 4. Example :2 Find δ=(q,a) Find δ=(q,b) Find δ=(q,c)
- 5. Find δ=(r,a) Find δ=(r,b) Find δ=(r,c)
- 6. Find δ=(s,a) Find δ=(s,b) Find δ=(s,c)