The number of states in the minimum sized DFA that accepts the language defined by the regular expression $$(0+1)^*(0+1)(0+1)^*$$ is ___________ .

The given regular expression is:

This represents the set of all strings over $\Sigma = \{0, 1\}$ containing at least one symbol (i.e., $(0+1)^+$), or equivalently, all strings except the empty string $\epsilon$.

A minimum DFA to recognize this language requires $2$ states:

1. State $q_0$ (Start state, non-accepting):

   • On input $0$ or $1$, it transitions to state $q_1$.

2. State $q_1$ (Accepting state):

   • On input $0$ or $1$, it self-loops at $q_1$.

Since strings of length $0$ ($\epsilon$) are rejected and strings of length $\ge 1$ are accepted, $2$ states are necessary and sufficient.

Therefore, the number of states in the minimum DFA is 2.