Suppose we modify the definition of a Finite Automaton to allow multiple starting states. That is, a modified Nondeterministic Finite Automaton (NFA) is defined with a set of start states $Q_0 \subseteq Q$ instead of a single start state $q_0$.
Does this modification increase the expressive power of the automaton?
Specifically:
1. Does this modified NFA recognize any non-regular languages?
2. Can a standard DFA be converted into a modified DFA with multiple start states, and vice versa?
Please explain with a construction showing how the start states transition works.