DFA / NFA Problems

1. Find dfa for the following language on Σ = {a, b} L = {ab4wb2: w ∈ {a, b}* }
2. A run in string is a substring of length at least two, as long as possible and consisting entirely of the same symbol. For instance, the string abbbaab contains a run of of b’s of length three and run of a’s of length two. Find dfa for the following language on {a, b}. L = {w: w contains no runs of length less than four}
3. Construct dfa that accept strings on {0, 1} if and only if the value of the string, interpreted as a binary representation of an integer, is zero modulo five. For example, 0101 and 1111, representing the integers 5 and 15, respectively are to be expected.