Informally speaking, a state function is a decision variable whose value is a set of non-overlapping intervals over which the function maintains a particular non-negative integer state. In between those intervals, the state of the function is not defined, typically because of an ongoing transition between two states.

For instance a state function could be used to describe the evolution of an oven's temperature over time. Assuming there are 3 possible temperature levels (indexed by 0, 1 and 2), a fixed value for this state function could be the following set of non-overlapping valued intervals:

• [start=0, end=100): state=0,
• [start=150, end=250): state=1,
• [start=250, end=300): state=1,
• [start=320, end=420): state=2,
• [start=460, end=560): state=0, ...

A set of constraints are available to restrict the evolution of a state function. These constraints allows specifying:

• That the state of the function must be defined and should remain equal to a given state everywhere over a given fixed or variable interval (IAlwaysEqual).
• That the state of the function must be defined and should remain constant (no matter its value) everywhere over a given fixed or variable interval (IAlwaysConstant).
• That intervals requiring the state of the function to be defined cannot overlap a given fixed or variable interval (IAlwaysNoState).
• That everywhere over a given fixed or variable interval, the state of the function, if defined, must remain within a given range of states [vmin, vmax] (IAlwaysIn).

For more information on state functions, see the concept LINK:CONCEPT_STATE.