Show understanding of the purpose of state-transition diagrams to document an algorithm

12.2 Program Design – State‑Transition Diagrams

Purpose of State‑Transition Diagrams

State‑transition diagrams (STDs) provide a visual representation of an algorithm’s behaviour. They show:

• All possible states the algorithm can occupy.
• Transitions triggered by inputs or events.
• The resulting state after each transition.

This abstraction helps students reason about control flow, detect missing cases, and verify correctness before coding.

Key Elements of an STD

• State – A distinct configuration of the system, usually labelled with a name or symbol (e.g., S0, Idle).
• Transition – A directed arrow from one state to another, annotated with the event or condition that causes the move.
• Initial State – The state where execution starts, marked with a single arrow pointing to it.
• Final/Accepting State – States where the algorithm terminates or achieves its goal, often indicated with a double‑circle.
• Guard Conditions – Boolean expressions that must be true for a transition to fire.

Constructing a State‑Transition Diagram

1. Identify the problem domain. Write a brief specification of the algorithm’s purpose.
2. Determine the states. List all distinct situations the algorithm can be in.
3. Define events. Note the inputs or internal triggers that can change the state.
4. Draw the states. Use circles or rounded rectangles, label them clearly.
5. Add transitions. Draw arrows between states, annotate with event and guard.
6. Mark initial and final states. Use the appropriate symbols.
7. Validate. Check that every possible event is accounted for and that the diagram is deterministic.

Example: Simple Login System

The algorithm manages user authentication. States and transitions are:

• Idle – Awaiting input.
• Checking – Verifying credentials.
• Authenticated – User logged in.
• Failed – Incorrect credentials.

Transitions:

• Idle → Checking on submit event.
• Checking → Authenticated if credentials == valid.
• Checking → Failed if credentials != valid.
• Failed → Idle on retry event.

Benefits of Using STDs

• Clarifies the algorithm’s control flow before implementation.
• Facilitates communication between designers and developers.
• Assists in identifying unreachable or duplicate states.
• Provides a basis for automated testing by enumerating all transitions.

Common Mistakes to Avoid

1. Omitting an initial or final state.
2. Using ambiguous or overlapping state names.
3. Failing to label guard conditions on transitions.
4. Allowing nondeterministic transitions (two arrows from the same state with the same event).
5. Neglecting to consider error or exceptional states.

Summary Table

Aspect	Description
State	Distinct configuration; represented by a circle.
Transition	Directed arrow; annotated with event and guard.
Initial State	Single arrow pointing to the start state.
Final State	Double‑circle; indicates algorithm termination.
Guard Condition	Boolean expression; must be true for transition.
Determinism	Only one transition per event from a given state.