Communicating Automata
The Component automata has the following general form:
( L, TL, T, l0) where
• L is a finite set of locations; the automaton can only be in one location at a time ;
• TL is a finite set of transition labels;
• T ⊆ L×TL×L is the transition relation, where (l, a, l) ∈ T states that a transition from location l to location l exists, which is labeled with a Transitions are typically denoted
Communicating Finite Automata
• In previous examples , we are using binary synchronization , also , we distinguish between instances of half actions, indicated by the symbols ! and ?, and completed actions, denoted without input/output annotations.
• a further reason for introducing communicating automata and binary synchronization is that they play a particularly important role in the timed concurrency theory setting, where timed automata, and their associated model-checking algorithms, are one of the most commonly used methods for specifying and verifying time critical systems.
Parallel Composition Basic Notation
• A parallel communicating Finite automata system is an accepting device based on the communication between more Finite automata working in parallel.
• It generates a single automaton from a vector of interacting component automata.
• This single automaton characterizes the global behavior that results from running the component automata in parallel.
• The automaton that arises from this parallel composition is called the product automaton.
Product Automaton Example
• Consider Product Automaton Example is Fragments of each of the two components of the communication protocol shown in Example 1.
• These fragments have been extracted from the components by removing all half actions that synchronize with components other than the sender and medium.
Product Automaton Example
• The resulting product automaton (denoted | [Sender ', Medium ']) characterizes the global behavior of the network, the product only contains completed actions.
• Thus, the rather degenerate behavior of the product is for a message to be sent, followed by an interleaving of the message being lost at the medium and the sender timing out. This sequence is repeated ad infinitum.
Question
• Draw the product Automaton that generates from Sender and Medium automaton in network of CA (communicating Automata ) .
• Answer : In Slide 9