Visual Formalisms
Message Sequence Charts
Book: Chapter 10
MSCs
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An ISO standard notation (Z120).
Visual + Textual forms.
Specifies behaviors of communication
protocols.
Existing algorithms + tools.
MSC visual notation
P1
P2
P3
M1
M2
M3
M4
M5
M6
MSC Textual form
msc MSC;
inst P1: process Root,
P2: process Root,
P3: process Root;
instance P1;
out M1 to P2;
in M5 from P2;
in M6 from P3;
endinstance;
instance P2;
in M1 from P1;
out M2 to P3;
out M3 to P3;
in M4 from P3;
out M5 to P1;
endinstance;
instance P3;
in M2 from P2;
in M3 from P2;
out M4 to P2;
out M6 to P1;
endinstance;
endmsc;
P1
M1
M5
P2
P3
M2
M3
M4
M6
Partial order semantics
s M1
r
s
M2
r
M3
r
r
M1
s
M4 s
r
M5 s
r M6
P1
M5
P2
P3
M2
M3
M4
M6
s
HMSCs
P1
P2
P3
P2
P3
P2
P3
approve
connect
P1
P1
P2
P3
fail
report
P1
req_service
Visual semantics
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Sends before corresponding receives.
Events on the same process line
execute in order of appearance, from
top to bottom.
Visual order (wysiwyg)
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If some event
(send, receive) is
higher on the line
than another, it
comes first.
Sends precede
matching
receives.
P1
M1
M5
P2
P3
M2
M3
M4
M6
Visual order (wysiwyg)
s M1
r
s
M2
r
M3
r
P1
s
M4 s
r
M5 s
r M6
r
s
M1
M5
P2
P3
M2
M3
M4
M6
Races
P1
M1
M5
P2
P3
M2
M3
M4
P1
M1
M6
P2
P3
M2
M3
M4
M6
M5
Causal Order and Races
•Sends before matching receive.
•Receive or sends before sends of
same process.
•Two receives on the same process
sent from the same process.
P1
M1
M5
P2
P3
M2
M3
M4
M6
Races: check if every pair of events ordered by the visual order
appears in the transitive closure of the causal order.
Causal Order
s M1
r
s
M2
r
M3
r
r
r
M6
s
M1
s
M4 s
r
M5
P1
s
M5
P2
P3
M2
M3
M4
M6
Calculating the transitive
closure
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Structure (E, R).
E – Events, R  E  E.
R* The transitive closure. Defined as
follows:
a R*b if there is a sequence
x1 x2 … xn where a=x1, b=xn,
and xi R xi+1 for 1i<n.
Complexity: cubic. In our case: quadratic
(every event has 1 or 2 successors).
Races for HMSCs
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Undecidable [MP99]
Idea of proof:
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Trasnlate to language theory of semitraces,
which are closed w.r.t. commuting certain
pairs of letters.
Intuition: moving from visual to causal
semantic introduces more commutations.
Reduction to universality of semitrace
languages.
Visual concatenation
P1
P2
P3
connect
fail
report
connect
fail
report
connect
approve
A
B
P1
P2
P3
P2
P3
approve
connect
P1
P1
P2
P3
P1
P2
P3
fail
req_service
report
Execution: concatenation of a
maximal path in the HMSC.
C
D
Model checking
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Write both specification and system as
HMSCs. Do concatenation.
Write specification in LTL. Interpret over
the linearizations of the partial orders.
In both cases: undecidable.
Post Correspondence Problem
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List of pairs:
w1:(aab,aa), w2:(aba,ab), … wn:(a,bb).
Want to find if we find a set of indexes
i1, i2, …, ik, such that concatenating
the lefthand words and concatenating
the righthand words is the same.
Supose we take indexes 1, 2, n, 1. We get:
lefthand: aab aba a aab
righthand: aa ab bb aa
PCP reduction
Letter match
Word
P5
match
P6
P1 a P2
P5
P1
a
b
P3
P4
P3
(ab,bab),...
P2
P5
P6
P1
P2
P1
b P2
a
b
P4
P3
P4
b
b
P4
w2
w1
(aab,bb),
a
b
P6
P3
w1
w2
P5
P6
Some solutions:
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Obtain decidability under the following
condition [MP99,AY99]:
Every HMSCs cycle covers a strongly
connected component in the dependency
graph, where events are dependent if they
belong to the same process or message.
The specification HMSCs allows any
additional messages [MPS98].
Put limit on message queues [Holzmann]