Loops and Branches

A programming language without loops and branches would be nearly useless. The same is true for finite-state automata. The new example automaton has two transitions out of the start state and has a loop between state q₁ and itself and a loop between states q₀ and q₂.

This automaton has two final states. This is OK. An automaton must have only one start state, but can have one or more final states. A string is accepted if its last character is consumed by a transition that leads to any final state.

The example input string is accepted by this automaton. The loop at state q₁ accepts any number of character 'b', including zero.