⚙ State Machines & Control Logic

What Is a Finite State Machine?

A Finite State Machine (FSM) is a mathematical model of a system that can be in exactly one of a finite number of states at any time. It transitions between states in response to inputs (events).

An FSM has five elements: a set of states, an initial state, a set of inputs (events), a transition function (what state to go to given current state and input), and a set of outputs (actions).

State Diagram Notation

• States: Circles or rounded rectangles labeled with the state name
• Initial state: Marked with an arrow from a solid circle (filled dot)
• Transitions: Arrows between states labeled "event / action"
• Final/accepting states: Double circles (used in formal language theory)

Moore vs. Mealy Machines

• Moore machine: Output depends only on the current state. Actions are written inside the state circle. Simpler to understand and debug.
• Mealy machine: Output depends on both the current state and the input. Actions are written on the transition arrows. More compact — fewer states needed.