Co-algebraic Model of Connectors Sample Clauses

Co-algebraic Model of Connectors. The co-inductive calculus of timed data streams first proposed in [27] and then extended to the notion of Abstract Behavior Types (ABT in short) [14], is a simple and transparent relational model of Reo. In this calculus the behavior of a connector port is modeled as a timed data stream. As we showed in Definition 3.2, an element of the time-stream is the time at which its respective data value in the data-stream is observed at its corresponding port. The interactions of connectors are modeled as relations on timed data streams. More formally, let TDS be the set all timed data streams, then each basic connector, namely channel, is defined as a binary relation R ⊆ TDS × TDS over timed data streams. For example, the synchronous channel of Reo (Sync) is modeled by the following relation: Sync = {(⟨α, a⟩, ⟨β, b⟩) | α = β ∧ a = b} ⟨ ⟩ ⟨ ⟩ where α, a and β, b respectively are the timed data streams over input and output ports of the channel. Because the connectors are relations, their composition is modeled by relational compo- sition. For example, the composition of two copies of the synchronous channel yields the following binary relation over the set TDS : Sync ◦ Sync = {(⟨α, a⟩, ⟨β, b⟩) | ∃⟨γ, c⟩: (α = γ ∧ a = c) ∧ (γ = β ∧ c = b)} This co-inductive model abstracts away from the connector topology, and the direction of the dataflow within the connector. Connectors are reduced to a collection of ports, and the behavior of the component-based system is expressed as a relation. Based on the relational nature of this semantics of Reo, if someone be interested to verify some properties of the com- munication protocol modeled by composed connectors, it should be done using a deductive verification method, as for a simple example it has been done in [27]. These models of Reo were shown to be equivalent to constraint automata, and thus unable to express several fairness constraints and context dependencies [36, 37]. Also, because the model is not an operational model it is not suitable for model checking based verification.
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