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Live State Machine

UML statechart

A traffic-signal controller drawn as a genuine UML state machine — initial pseudostate, three states, four guarded transitions. Firing an event (or letting the timer run) moves a live token: the active state glows, the taken transition pulses, and an event-trace log records the run. The diagram is not a picture of the machine; it is the machine.

4 components · 4 connections · event-driven finite-state executor

the aha
The boxes-and-arrows diagram is not documentation of the machine — run an event through it and it is the machine.

why it works

A finite-state machine is a transition function

\delta : S \times \Sigma \rightarrow S

: given the current state

s

and an event

e

, it names exactly one next state — but only if the transition’s guard is satisfied. That is the whole of it. A traffic light is

S = \{\text{Red}, \text{Green}, \text{Yellow}\}

and the events are timer expiries. What schemd lets you see, that a textbook cannot, is that the drawing and the behaviour are the same object: the token sitting on Red is the machine’s state, and firing

t > T_{red}

literally advances

\delta

along the arrow you drew. Composability, unreachable states, and deadlocks stop being abstractions — they are places the token can or cannot go.

governing model

\delta : S \times \Sigma \rightarrow S \;\cdot\; (s, e) \mapsto s_{\text{next}} \text{ if guard}(e)

structural inventory

initial pseudostate
Red / Green / Yellow states
4 guarded transitions
event queue + trace log

boundaries

deterministic $\delta$
one active state
guarded, timed transitions

fault relay transition guard inverted (deadlock)

Fire the timer events in sequence.

Red → Green → Yellow → Red. The active state glows and each taken transition pulses; the trace log is the exact run $\delta(\delta(\delta(s_0, e_1), e_2), \dots)$ .
Try to fire an event with no matching transition.

Nothing happens — and that nothing is meaningful. A well-formed machine simply has no arrow for an impossible input; the token holds.
Invert a guard.

Flip one transition’s condition and the machine reaches a state it can never leave — a deadlock. You are watching a liveness bug happen, not reading about one.

causal signal trace paused

Enter the machine Power-on follows the initial transition into Red.

t_{stage} = 0.00 s

step 1 / 4 Enter the machine

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