This document discusses communicating finite automata and their parallel composition. It defines the components of a finite automaton and provides examples of communicating finite automata. It then explains that parallel composition generates a single automaton from interacting component automata, called the product automaton. The document provides an example product automaton generated from two interacting components, showing the global behavior that results from their parallel execution. It concludes by asking the reader to draw the product automaton generated from two specific communicating finite automata.

1. Communicating
Finite Automata
Rehan Hattab
Computation Theory
Master Course -2013- JU

2. Communication Protocol

3. 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

4. Example 1

5. Example 2

6. 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.

7. 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.

8. 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.

9. Product Automaton Example

10. 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.

11. Question
• Draw the product Automaton that generates from Sender and
Medium automaton in network of CA (communicating
Automata ) .
• Answer : In Slide 9

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