Understanding Deterministic Finite Automata (DFA) for Strings Ending with Specific Patterns | Example Series 📘

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(i) Strings over {a, b} ending in aa.
(ii) String over {a, b} containing three consecutive a’s (that is, contains the substring aaa).
(iii) Strings over {a, b} not containing the substring aaa.
(iv) All strings over {a, b} where each string of length 5 contains at least two a’s.
(v) The set of strings over {a, b} where each pair of a’s immediately succeeds a pair of b’s.
(vi) The strings ε, 001 and 000101.
(vii) Strings over {0, 1} beginning with a 1 and which, if interpreted as a binary number, is a multiple of 5. As an example, the string 1010 should be accepted since 1010, which is a multiple of 5. On the other hand, the string 1110 should not be accepted, since 1110
which is not a multiple of 5.
(viii) {w ∈{a, b}∗ ||w|
a
=2n, |w|
=2m, m, n ∈ N}
(ix) {w ∈{a, b}
∗
||w|
a
b
=3n, n ∈ N} and w doesn’t contain the substring aba.

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