A run in a string is a substring of length at least two, as long a possible, and consisting entirely of the same symbol. For instance, the string abbbaab contains a run of bs of length three and a run of as of length two. Find dfas for the following language on {a,b}, such that L = {w: every run of as has length either two or three}

Recall: A deterministic finite accepter or DFA is defined by the 5-tuple

M = (Q, , S, q₀, F), where

Q is a finite set of internal states

is a finite set of symbols called the input alphabet

S : Q x Q is a total function called the transition function

q₀ Q is the initial state

F Q is a set of final states

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