Guarded Languages and Augmented Bu¨ chi Au Sample Clauses

Guarded Languages and Augmented Bu¨ chi Au tomata In this section we augment our model for component connectors so to take into account context dependencies like the ones of the lossy synchronous channel: if the port connected at the source is ready for accepting data but the port at the sink it is not ready for receiving it, then the data at the source is lost. In the previous chapter, we have ignored such a requirement and modeled the loss of data by means of a (fair) non-deterministic choice with a BAR. In this section, we extend Bu¨chi automata of records with the capability of modeling coordination strategies based on pending and ignored ports. The idea is to enrich the states of a BAR automaton with expressions for testing if the ports shared with the environment are ready to communicate or not. Intuitively, a transition q −r→ p can be taken only if the ports of the system successfully pass the test associated with a state q . This implies that we must be able to safely eliminate states associated with tests that always fail, and that passing a test has to guarantee that at least as many ports are ready to communicate as needed by every outgoing transitions. More formally, we consider the set N of port names as our primitive test symbols. Next, we define the set ExpN of expression for Boolean tests for N as follows: Definition 5.1 Let N be a set of port names. The set ExpN of expression for Boolean tests for N is defined by the grammar e :: = 1 | 0 | A| A¯ | e · e where A ∈ N . ∈ ⊆ N Each test expression e ExpN is evaluated over a set N of ports (ready to com- municate):