Automata

Alphabet

There are a set of states $Q$. If it's finite, then it's a Finite State Machine
There are a set of actions/operations that allow from moving between states.
There is a transition function/relation that allow movement between states using actions/operations

Deterministic Automation is a 5-tuple

where: $\mathrm{\Sigma }$ is the alphabet
$Q$ is the set of states
$\delta :Q\times \mathrm{\Sigma }\to Q$ is transition function
$s_0\in Q$ is the initial state
$F\subseteq Q$ is the set of final states

Deterministic means that the next transition is predetermined (always known) given the current state

Finite State Automata

See also: NieR Automata