Occurrences of input and output signals of an actor with particular moments of time when those occurrences took place is the event history of the actor.
An example event history along with changing spur values represented as a two-dimensional chart is in Figure 2.1.
In the chart, filled dots denote events of receiving input signals, and unfilled dots denote events of emitting output signals. Every such event is on a horizontal line denoting a particular input or output signal with an identifier printed after the line end. In QSMM 1.18, a set of input signal identifiers and a set of output signal identifiers ordinarily do not overlap. Every input signal and its corresponding output signal connected by an arrow are on the same vertical line, as the API does not specify the time between receiving an input signal and emitting an output signal by an actor. A plot of single spur value change over time is above the event history.
A fragment of this two-dimensional chart in gray represented as a one-dimensional plot is in Figure 2.2.
We may assume that every event of receiving an input signal encodes an event of receiving a tuple of signals. Identifiers assigned to unique tuples would be input signal identifiers.
For example, we can replace every input signal with a triple of signals. The event history fragment with input signals replaced with triples of signals is in Figure 2.3.
In this figure, input signal 3 has encoded triple <3, 0, 4>, input signal 5 has encoded triple <1, 2, 5>, and input signal 0 has encoded triple <5, 3, 3>.
In this way, by setting one-to-one correspondence between single-value arguments of a probabilistic mapping and n-value tuples, we convert the mapping to an n-ary probabilistic mapping.
By including the previous outcome of a probabilistic mapping in its next n-ary argument, we convert a stateless probabilistic mapping to a stateful mapping—an outcome of a probabilistic mapping becomes its state; in this way, the probabilistic mapping can model a finite automaton. After this conversion, input signal 5 encodes quadruple <21, 1, 2, 5>, and input signal 0 encodes quadruple <19, 5, 3, 3>.
An n-ary argument of an adaptive probabilistic mapping is an action choice state of an actor. An action choice state is an input list of events an actor shall respond to by choosing an action—emitting an output signal. An action choice state might be a guessed or known current system or environment state that requires generating an adaptive action.
In the past, action choice states were meant to be n-grams of events from an event history. The current view is that action choice states are not necessarily n-grams, but the terminology remains the same for compatibility. An action choice state n-gram is a signal identifier list that encodes an action choice state. The tuples <3, 0, 4>, <1, 2, 5>, <5, 3, 3>, <21, 1, 2, 5>, and <19, 5, 3, 3> are action choice state n-grams used to select output signals 21, 19, and 17.