Construct a NFA , N= {Q, S, d, q0, F}, S ={0,1}, that recognize the language:

L = { w/w contains 2 consecutive identical digits}

Hint: (a) start with q0 and define two paths depended on the input symbols, use transitions from the same input symbol to move to different states

- define 5 states , -q₀,q₁,q₂,q₃,q₄,q₅-

- create the transition table

b. find if the word 01001 is accepted from the NFA (formal proof)

Hint: start with d^h (q₀,01001),

c. find if the word 0100011 is accepted from the NFA (formal proof)

d. give the states of the NFA (stuck, threads) for any input digit of the 0100011