Finite State Machine

Gold definitionUpdated Apr 2, 2026

Definition

A Finite State Machine (FSM) is a mathematical model representing a system's behavior through a finite number of states, transitions between them, and actions. It provides a deterministic way to model sequential logic, crucial for designing predictable control systems.

At a glance

Executive summary

Finite State Machines are a way to model systems that have a limited number of distinct conditions or "states" and move between them based on specific events. They are useful for designing predictable control logic, like for autonomous vehicles, where they can provide a reliable starting point for more advanced AI.

TL;DR

A Finite State Machine is a model that describes how a system changes between a fixed number of defined states based on specific triggers.

Key points

Models system behavior using a finite set of states and transitions triggered by events
Provides a clear, deterministic, and interpretable way to design and analyze sequential logic and control flow
Used by software engineers, game developers, embedded systems designers, and AI researchers (e.g., for expert policies in RL)
Unlike neural networks which learn complex, continuous mappings, FSMs offer explicit, discrete, and rule-based control
Increasingly used as foundational expert policies or for defining safety envelopes in hybrid AI systems, especially in robotics and autonomous systems

Use cases

Traffic Light Control: Each light (red, yellow, green) is a state, and timers or sensor inputs trigger transitions.
Game AI: Character behaviors (e.g., idle, walking, attacking, fleeing) are states, with player actions or game events triggering transitions.
Network Protocols: Defining the sequence of messages and states for communication protocols like TCP.
Lexical Analysis in Compilers: Recognizing tokens (keywords, identifiers, numbers) based on sequences of characters.
Autonomous Vehicle Behavior: Defining high-level behaviors like "lane following," "obstacle avoidance," or "parking" as states, with sensor inputs and planning outputs triggering transitions.

Also known as

FSM, State Machine, Finite Automaton, Mealy Machine, Moore Machine, State Chart