give a formal definition of the string accepted by an NFA and ε-NFA . Design a DFA that accepts all strings over {0, 1}

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give a formal definition of the string accepted by an NFA and ε-NFA
. Design a DFA that accepts all strings over {0, 1} that have 101 as a substring, where k is a substring of w if there are w1 and w2 such that w = w1 k w2.
. Convert the DFA in Q3 above to an equivalent NFA
. Below is an ε-NFA that models a new vending machine proposed at Legon Supermarket;
a) Determine the set of substrings accepted by the ε-NFA above
b) Determine the ε-closure of all possible states of the ε-NFA above
c) Derive the state transition table associated with the ε-NFA above