In this article, we delve into the relationship between activities and events in the context of I/O automata. We explore how a sequence of activities can be combined using an operator called the sequencing operator to obtain the activity of a behavior. Moreover, we discuss how events emitted by an activity may have their outcomes resolved by the plant, but the deterministic I/O automaton only processes a single event at each branching state. We then introduce a function that extracts the sequence of (event, outcome) pairs from any given accepted word of the automaton.
Activities and Events
An activity is a quadruple consisting of a DAG (directed acyclic graph), a set of nodes, a set of dependencies, and a set of event outcomes. The sequencing operator allows us to combine a sequence of activities into a single activity, giving the same order and timing of action and event nodes. This enables us to model complex behaviors by combining simpler activities in a systematic way.
Processing Events
In contrast, events emitted by an activity may have their outcomes resolved by the plant, but the deterministic I/O automaton only processes a single event at each branching state. This means that the sequence of (event, outcome) pairs from a behavior is important in determining the order in which event outcomes are processed. To extract this sequence, we define a function called the processed events function, which takes an accepted word of the automaton and returns the corresponding sequence of (event, outcome) pairs.
Conclusion
In conclusion, this article has explored the relationship between activities and events in I/O automata, as well as the sequencing operator’s role in combining activities into a single activity. We have also discussed how events emitted by an activity may have their outcomes resolved by the plant, but the deterministic I/O automaton only processes a single event at each branching state. Finally, we introduced a function that extracts the sequence of (event, outcome) pairs from any given accepted word of the automaton. By understanding these concepts, we can better model complex behaviors and design more efficient systems.
