Communicating Finite Automata

Rehan Hattab Computation Theory Master Course -2013-

JU

Communication Protocol

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

Example 1

Example 2

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

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

Reference

H.Bowman R.Gomez , Concurrency Theory: Calculi an Automata for Modelling Untimed and Timed Concurrent SystemsSpringer-Verlag New York, Inc. Secaucus, NJ, USA ©2005