2.1 Event History ¶
Occurrences of input and output signals of an actor with particular moments of time when the occurrences took place is an actor’s event history.
An example event history along with changed spur values represented as a two-dimensional chart is in Figure 2.1.
Figure 2.1: an event history example as a two-dimensional chart
In the chart, filled dots denote the events of receiving input signals, and unfilled dots denote the 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. Every input signal and its corresponding output signal connected by an arrow are on the same vertical line, as the API does not specify time between receiving an input signal and emitting an output signal by an actor. A plot of single spur value changing 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.
Figure 2.2: an event history fragment as a one-dimensional plot
We can consider that every event of receiving an input signal encodes an event of receiving a tuple of signals. Identifiers assigned to unique tuples will be input signal identifiers.
For example, we can replace every input signal with a triple of signals. The above event history fragment changed to show input signals replaced with signal triples is in Figure 2.3.
Figure 2.3: tuples of signals as input signals
In this figure, input signal 3 has encoded the triple <3, 0, 4>, input signal 5 has encoded the triple <1, 2, 5>, and input signal 0 has encoded the triple <5, 3, 4>.
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 stateful one—an outcome of a probabilistic mapping becomes its state. Using this approach, a probabilistic mapping can model a finite automaton. After the conversion, input signal 5 encodes the quadruple <5, 1, 2, 5>, and input signal 0 encodes the quadruple <3, 5, 3, 4>, where the first 5 in the first quadruple is a previous state of the probabilistic mapping, and the first 3 in the second quadruple is the next state.
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 known or guessed 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 encoding an action choice state. The tuples <3, 0, 4>, <1, 2, 5>, <5, 3, 4>, <5, 1, 2, 5>, and <3, 5, 3, 4> are action choice state n-grams used to select output signals 5, 3, and 1.