A-Level Computer Science 9618 / Topic 12 / AS

Every input, a new state.

Some programs do not run from start to finish: they wait, react to an event, and wait again. A car alarm, a lift or a login screen behaves differently depending on what has already happened. A state-transition diagram documents exactly how such a system moves from one state to another.

Full-screen labPseudocode lab → Topic 12All software development lessons →

The key idea

A state-transition diagram documents an algorithm or system whose behaviour depends on its current state and the next input (event). Each state is a circle. Each transition is an arrow from one state to another, labelled with the input that causes it and, after a slash, any output it produces: input / output. An arrow from a dot marks the start state; a double circle marks a halting (final) state. The same information can be written as a state-transition table.

Fig. 1: the alarm starts Disarmed; locking arms it; opening a door while armed sounds the siren; unlocking always disarms it

Section 01

States and transitions.

Follow Fig. 1 with your finger. Start at the dot: the alarm is Disarmed. Input "lock" moves it to Armed. Now "door opened" moves it to Sounding and outputs "siren on". Only "unlock" gets it back to Disarmed.

State: the condition the system is in at a moment, which decides how it responds to the next input (Disarmed, Armed, Sounding).
Transition: a change from one state to another, triggered by an input or event. The arrow can loop back to the same state.
Input / output label: door opened / siren on means: on input door opened, output siren on and move along the arrow.
Start state: shown by an arrow coming from a dot (or from nowhere). Halting state: a double circle; the system stops there.
Purpose: to document, clearly and completely, how a system responds to every input in every state, so the design can be checked (for example, is any input in any state left undefined?) and then coded.

Examiner trap

Label every arrow with the input that causes it. An arrow with no label, or a state with no way out when the system should continue, loses marks.

Section 02

Tables and traces.

A state-transition table lists one row for each arrow. To trace a diagram, start in the start state and follow one arrow for each input in turn.

Current state	Input	Output	Next state
Disarmed	lock	none	Armed
Armed	unlock	none	Disarmed
Armed	door opened	siren on	Sounding
Sounding	unlock	siren off	Disarmed

Fig. 2: a door keypad allows three wrong PINs; the third wrong PIN locks it permanently

Worked example Trace a sequence

The keypad in Fig. 2 receives the inputs wrong, wrong, correct. Give each state it passes through and the final state.

Start state: 0 fails.
wrong: 0 fails moves to 1 fail.
wrong: 1 fail moves to 2 fails.
correct: 2 fails moves to Open, a halting state.

Answer: 0 fails, 1 fail, 2 fails, Open: the door opens

Your turn

What is the final state of the keypad in Fig. 2 after the inputs wrong, wrong, wrong, correct?

Stage 1 · Learn

Check what the sim just showed you

Four quick checks. Each correct answer earns XP and records this skill on your profile.

Quick check+10 XP

On a state-transition diagram, what does a circle represent?

Quick check+10 XP

In Fig. 1, what is the state after the inputs lock, unlock, lock?

Quick check+10 XP

How is a halting state shown?

Quick check+10 XP

A transition is labelled coin / unlock. What does this mean?

Section 03

From diagram to code.

A state-transition diagram converts directly into pseudocode. Store the current state in a variable; for each input, a CASE statement on the state decides which transition (if any) to make.

DECLARE State : STRING
State ← "Disarmed"

PROCEDURE HandleEvent(Event : STRING)
    CASE OF State
        "Disarmed" : IF Event = "lock" THEN
                         State ← "Armed"
                     ENDIF
        "Armed"    : IF Event = "unlock" THEN
                         State ← "Disarmed"
                     ELSE
                         IF Event = "door opened" THEN
                             State ← "Sounding"
                             CALL SirenOn()
                         ENDIF
                     ENDIF
        "Sounding" : IF Event = "unlock" THEN
                         State ← "Disarmed"
                         CALL SirenOff()
                     ENDIF
    ENDCASE
ENDPROCEDURE

One CASE branch per state, one IF per arrow leaving that state.
Outputs on the arrows become the actions (here, procedure calls) done during the transition.
An input with no arrow from the current state (for example lock while Sounding) changes nothing: no branch matches it.

Your turn

Using Fig. 1, what is the state and what is output after the inputs lock, door opened, lock, unlock?

Examiner trap

Do not confuse a state-transition diagram with a flowchart. A flowchart shows the steps of a process in order; a state-transition diagram shows states and the inputs that move the system between them.

Stage 2 · Exam

Exam-style questions

Unlocks once the four checks above are done. Worth more XP, written to AS Paper 1 and Paper 2 standard.

Finish the four checks above to unlock the exam questions

Exam style+20 XP

What is the purpose of a state-transition diagram?

Exam style+20 XP

In Fig. 2, the keypad receives wrong, correct. What is the final state?

Exam style+20 XP

A state-transition table has the row: Armed, door opened, siren on, Sounding. Which column holds "siren on"?

Exam style+20 XP

When a state-transition diagram is coded in pseudocode, which construct most directly selects what to do for the current state?

Skill unlocked

State-transition diagrams, mastered.

This skill is now recorded on your profile. Keep the chain going.

-Rank -Level -Score -Topics

Go deeper · practice

Six original Cambridge-style questions

States, transitions, input / output labels, start and halting states, state-transition tables, traces and pseudocode.