1. Let Σ = {0, 1} be an alphabet. (a) Let w = 101 be a word over Σ. Compute |w|, the length of w. (b) List all of the words in Σ3
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1. Let Σ = {0, 1} be an alphabet.
(a) Let w = 101 be a word over Σ. Compute |w|, the length of w.
(b) List all of the words in Σ3
2. Let {a, b, c} be an alphabet. List all of the words in Σ2
3. Let Σ = {a, b} be an alphabet and let · denote concatenation. Compute (ba · ε) · abb,
where ε is the empty word.
4. Let Σ = {0, 1} be an alphabet and let L ⊆ {0, 1} ∗ be the language defined as L = {w ∈ {0, 1} ∗ |w = x10y, x, y ∈ {0, 1}∗}.
(a) Determine whether 01 ∈ L.
(b) Determine whether 0101 ∈ L.
5. Let Σ = {0, 1} be an alphabet and let L ⊆ Σ ∗ be the language consisting of all words
over Σ that contain the substring 10. Construct a DFA that accepts L.
Thank you in advance
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Given that,
The language contains the input alphabets Σ = {0, 1}
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