CFSM: Communicating Finite State Machines
C1
1
+A
1
-R
2
Sender
-A
C2
1
Initial node with double
circle, every CSFM only
has one initial state
2
State of a CFSM
+R
2
Receiver
1
CFSM
CFSM
-R Transition of a CFSM
- sign in label  sending
Communicating Finite State Machine
+ sign in label  receiving
Is represented by states and transitions 2
string after signmsg type
and connected to channels.
This transition sends msg
Here sender machine has two channels:
R to the CFSM’s outgoing
C1 and C2. Channel are assumed to be FIFO.
channel.
C1 is the outgoing channel for sender.
It can also be represented
C2 is the incoming channel for sender.
as (1, 2, -R)
When the sending transition of sender fires,
It sends the msg in transition label to the outgoing channel.
The receiving transition can only occurs if there is a msg of the same type in
the head of CFSM’s incoming channel.
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Reachability Analysis
Page 1
Operation of CFSM
C1
1
current state
1
-R
+A
+R
-A
2
Sender
2
Receiver
C2
When the network starts, the current states of both machines are
set at their initial states.
Receiver at state 1 can not fire the outgoing transition (1, 2, +R)
Sender at state 1 can fire the outgoing transition (1, 2, -R), and
result in current state of sender changed to 2 and msg R is put in
channel C1.
C1
1
+A
-R
2
Sender
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1
R
-A
C2
Reachability Analysis
+R
2
Receiver
Page 2
Operation of CFSM: Step 2
C1
R
1
-R
+A
2
Sender
1
+R
-A
2
Receiver
C2
• Now sender at state 2 has (2,1,+A) as its outgoing transition.
There is no msg A in C2, therefore this receiving transition
cannot be fired. It waits.
• Receiver at state 1 checks its outgoing receiving transition
(1,2,+R) and found the msg label matched with the msg in the
head of C1. It fires the transition, takes in the msg R (removes
from C1) and changes its current state to state 2.
C1
1
+A
1
-R
2
Sender
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-A
C2
Reachability Analysis
+R
2
Receiver
Page 3
Operation of CFSM: Step 3
C1
R
1
-R
+A
2
Sender
1
+R
-A
2
Receiver
C2
• Now sender at state 2 has (2,1,+A) as its outgoing transition.
There is no msg A in C2, therefore this receiving transition
cannot be fired. It waits.
• Receiver at state 1 checks its outgoing receiving transition
(1,2,+R) and found the msg label matched with the msg in the
head of C1. It fires the transition, takes in the msg R (removes
from C1) and changes its current state to state 2.
C1
1
+A
1
-R
2
Sender
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-A
C2
Reachability Analysis
+R
2
Receiver
Page 4
Operation of CFSM: Step 4
C1
1
1
-R
+A
2
Sender
+R
-A
C2
2
Receiver
• Now sender still at state 2 has (2,1,+A) as its outgoing transition.
There is no msg A in C2, therefore this receiving transition cannot
be fired. It waits.
• Receiver at state 2 checks its outgoing sending transition (1,2,-A).
It fires the transition, put msg A in C2, and changes its current state
to state 2.
C1
1
+A
1
-R
2
Sender
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-A
A
C2
Reachability Analysis
+R
2
Receiver
Page 5
Operation of CFSM: Step 5
C1
1
1
-R
+A
2
Sender
+R
-A
A
C2
2
Receiver
• Receiver at state 1 checks its outgoing sending transition (1,2,+R).
There is no msg R in C1. It waits.
• Now sender at state 2 has (2,1,+A) as its outgoing transition.
There is a msg A in C2, therefore this receiving transition can be
fired. It reads in A (remove from C2) and changes state to 1. Now
Both machines get back to their initial states.
C1
1
+A
1
-R
2
Sender
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-A
C2
Reachability Analysis
+R
2
Receiver
Page 6
What could happen next?
C1
1
+A
1
-R
-A
2
Sender
+R
2
Receiver
C2
• In CFSM model, we assume only one transition can be
fired in a time. No two simultaneous firing.
Sender: (1,2,-R)
Receiver: (2,1,-A)
C1
C1
1
+A
1
1
-R
2
Sender
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-A
A
C2
+R
2
Receiver
+A
-R
2
Sender
Reachability Analysis
1
R
-A
C2
+R
2
Receiver
Page 7
What could happen next?
C1
R
1
+A
1
-R
-A
2
Sender
-B +R
2
Receiver
C2
• Sender cannot move.
• Receiver can either receive msg R or send msg B.
• How many msgs can be in C1 for this network? How
about C2?
Receiver: (1,2,-B)
Receiver: (1,2,+R)
C1
R
C1
1
+A
1
1
-R
2
Sender
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C2
-A -B +R
2
Receiver
+A
-R
2
Sender
Reachability Analysis
B
C2
1
-A -B +R
2
Receiver
Page 8
What could happen next?
C1
1
+A
1
-R
2
Sender
-A
C2
+R
2
Receiver
• Receiving state is a state where all its outgoing
transition are all receiving transition. It can not move
without msg in its incoming channel.
• Both machines are at receiving states and channels are
empty. This is called deadlock. The network can not
progress further.
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Reachability Analysis
Page 9
Unspecified Reception Error
C1
1
+A
1
-R
2
Sender
-A
B
C2
+R
2
Receiver
• There is msg B in C2 but sender does not have a
receiving transition with msg B.
• This is called unspecified reception. The network can
not progress further.
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Reachability Analysis
Page 10
Non-executable States and Transitions
C1
1
+A
1
-R
2
Sender
-A
B
C2
-C
+R
2
+B
Receiver
3
• State 3 of Receiver will never be executed or become
the current state. It is called non-executable state.
• Transitions (2,3,+B) and (3,1,-C) will never be executed.
They are called non-executable transitions.
• How does one know they will never be executed?
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Reachability Analysis
Page 11
Reachability Analysis
1 E gs0
E 1
A process of generating all possible
reachable states from the initial global state
-B
C1
1
+A
1
-B
-R
2
Sender
-A
C2
Sender’s
State
Channel C2’s
content
Channel C1’s
content
Receiver’s
State
global state/reachable state
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+R
2
Receiver
CFSM
CFSM
2 B
E 1
gsn
Global
State ID
-R
gs1
Unspecified
Reception
Receiver do
not know
how to receive B
E: channel empty
2 R gs2
E 1
+R
2 E
E 2
-A
2 E gs4
A 1
Reachability Graph
Reachability Analysis
gs3
+A
Page 12
Reachability Analysis
• Starting from initial global state, where channels are
empty and machines at their initial state, explore all
possible reachable state by firing the possible
transitions (and generating global states) from any
given reachable state.
• All deadlock and unspecified reception errors will be
captured/marked as individual global state.
• By examining the number of msgs in the channels we
can design the buffer size for the protocol.
• Can detect non-executable states and transitions by
marking those state are touched and transition that are
fired during the reachability analysis.
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Reachability Analysis
Page 13
Reachability Analysis Exercise
+A
-R
2
M
N
1
1
-A
+R
3
+A
-R
2
-A
+R
3
a) Perform the reachability analysis on the Network (M, N).
b) What sizes of buffers are needed for the two FIFO
channels?
c) Are there non-executable states or transitions?
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Reachability Analysis
Page 14
Solution
GS 0
1 E
E 1
• One unspecified reception.
N: -R
M: -R
• Both channels need
GS 2
GS 1
1 E
2 R
buffer size of 2.
R 2
E 1
N:-R M:- R
M:+R
(see gs8 and gs9)
N:+R
GS 4
GS 5
GS 3
• No non-executable
2
R
3 E
2 E
R 2
E 2
E 3
states and
unspecified
M:- A
N:-A
reception
transitions.
GS 6
GS 7
M:+A
2 E
1 A
• Since both machines
A 1
E 2
send same types
M:-R
N:-R
GS 8
GS 9
of msgs. We use
2 E
2 AR
AR 2
E 2
Machine: to specify
N:+A
M:+A
which machine fires
Figure 1. Reachability graph.
the transition.
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Reachability Analysis
Page 15
N:+A