Finite state machine (FSM)

• It's a computational model that describes a system with a fixed set of states, where transitions between states are triggered by inputs or events.

• It's a directed graph

• States - discrete configurations the system can be in (e.g., idle, loading, error)

• Transitions - rules for moving from one state to another
• Inputs/Events - what triggers a transition (e.g., submit, timeout)
• Initial state — where the machine starts (and optionally, accepting/final states)

Analysis

• Reachability analysis — graph traversal (BFS/DFS) can determine if a state is reachable from the initial state, or if dead states exist
• Cycle detection — identifies infinite loops (e.g., a retry loop that never terminates)
• Minimization — FSM minimization algorithms (like Hopcroft's) work on the graph structure to merge equivalent states
• Visualization — tools like Mermaid and XState render FSMs as literal node-edge diagrams