Define Chart Behavior by Using Actions

State and transition actions are instructions that you write inside a state or next to a transition to define how a Stateflow® chart behaves during simulation. For more information, see Model Finite State Machines.

For example, the actions in this chart define a state machine that empirically verifies one instance of the Collatz conjecture. For a given numerical input u, the chart computes the hailstone sequence n0 = u, n1, n2, n3, … by iterating this rule:

  • If ni is even, then ni+1 = ni / 2.

  • If ni is odd, then ni+1 = 3ni+1.

The Collatz conjecture states that every positive integer has a hailstone sequence that eventually reaches a value of one.

The chart consists of three states. At the start of simulation, the Init state initializes the chart data:

  • The local data n is set to the value of the input u.

  • The local data n2 is set to the remainder when n is divided by two.

  • The output data y is set to false.

Depending on the parity of the input, the chart transitions to either the Even or Odd state. As the state activity shifts between the Even and Odd states, the chart computes the numbers in the hailstone sequence. When the sequence reaches a value of one, the output data y becomes true and triggers a Stop Simulation block in the Simulink® model.

State Action Types

State actions define what a Stateflow chart does while a state is active. The most common types of state actions are entry, during, and exit actions.

Type of State ActionAbbreviationDescription
entryenAction occurs on a time step when the state becomes active.
duringduAction occurs on a time step when the state is already active and the chart does not transition out of the state.
exitexAction occurs on a time step when the chart transitions out of the state.

You can specify the type of a state action by its complete keyword (entry, during, exit) or by its abbreviation (en, du, ex). You can also combine state action types by using commas. For instance, an action with the combined type entry,during occurs on the time step when the state becomes active and on every subsequent time step while the state remains active.

This table lists the result of each state action in the hailstone chart.

StateActionResult
Init

entry:
 n2 = rem(n,2);
 y = false;

When Init becomes active at the start of the simulation, determines the parity of n and sets y to false.

exit:
 y = isequal(n,1);

When transitioning out of Init after one time step, determines whether n is equal to one.
Even

entry,during:
 n = n/2;
 n2 = rem(n,2);

Computes the next number of the hailstone sequence (n / 2) and updates its parity on:

  • The time step when Even first becomes active.

  • Every subsequent time step that Even is active.

Odd

entry,during:
 n = 3*(n-y)+1;
 n2 = rem(n,2);

Computes the next number of the hailstone sequence (3n+1) and updates its parity on:

  • The time step when Odd first becomes active.

  • Every subsequent time step that Odd is active.

Throughout most of the simulation, y evaluates to zero. On the last time step, when n = 1, y evaluates to one so this action does not modify n or n2 before the simulation stops.

Transition Action Types

Transition actions define what a Stateflow chart does when a transition leads away from an active state. The most common types of transition actions are conditions and conditional actions. To specify transition actions, use a label with this syntax:

[condition]{conditional_action}
condition is a Boolean expression that determines whether the transition occurs. If you do not specify a condition, an implied condition evaluating to true is assumed.

conditional_action is an instruction that executes when the condition guarding the transition is true. The conditional action takes place after the condition but before any exit or entry state actions.

This table lists the result of each transition action in the hailstone chart.

TransitionActionAction TypeResult
Default transition into Init

n = u

Conditional actionAt the start of the simulation, assigns the input value u to the local data n.
Transition from Init to Even

n2 == 0

ConditionWhen n is even, transition occurs. The number 1 at the source of this transition indicates that it is evaluated before the transition to Odd.
Transition from Init to Odd NoneWhen n is odd, transition occurs. The number 2 at the source of this transition indicates that it is evaluated after the transition to Even.
Transition from Odd to Even

n2 == 0

ConditionWhen n is even, transition occurs.
Transition from Even to Odd

n2 ~= 0

ConditionWhen n is odd, transition occurs.

y = isequal(n,1)

Conditional actionWhen transition occurs, determines whether n is equal to one.

Examine Chart Behavior

Suppose that you want to compute the hailstone sequence starting with a value of nine.

  1. In the Model Configuration Parameters dialog box, under Solver, select these options:

    • Start time: 0.0

    • Stop time: inf

    • Type: Fixed-step

    • Fixed-step size: 1

  2. In the Property Inspector, select the symbol n for logging.

  3. In the Constant block, enter an input of u = 9.

  4. Click the Run icon .

The chart responds with these actions:

  • At time t = 0, the default transition to Init occurs.

    • The transition action sets the value of n to 9.

    • The Init state becomes active.

    • The entry actions in Init set n2 to 1 and y to false.

  • At time t = 1, the condition n2 == 0 is false so the chart prepares to transition to Odd.

    • The exit action in Init sets y to false.

    • The Init state becomes inactive.

    • The Odd state becomes active.

    • The entry actions in Odd set n to 28 and n2 to 0.

  • At time t = 2, the condition n2 == 0 is true so the chart prepares to transition to Even.

    • The Odd state becomes inactive.

    • The Even state becomes active.

    • The entry actions in Even set n to 14 and n2 to 0.

  • At time t = 3, the condition n2 ~= 0 is false so the chart does not take a transition.

    • The Even state remains active.

    • The during actions in Even set n to 7 and n2 to 1.

  • At time t = 4, the condition n2 ~= 0 is true so the chart prepares to transition to Odd.

    • The transition action sets y to false.

    • The Even state becomes inactive.

    • The Odd state becomes active.

    • The entry actions in Odd set n to 22 and n2 to 0.

  • The chart continues to compute the hailstone sequence until it arrives at a value of n = 1 at time t = 19.

  • At time t = 20, the chart prepares to transition from Even to Odd.

    • Before the Even state becomes inactive, the transition action sets y to true.

    • The Odd state becomes active.

    • The entry actions in Odd do not modify n or n2.

    • The Stop Simulation block connected to the output signal y stops the simulation.

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