Regions
Finite Partitioning of State Space
y
2
1
1
2
3
x
An equivalence class (i.e. a region)
in fact there is only a finite number of regions!!
An Example Region Graph
Fischer’s Protocol
2
´
V
Init
V=1
A1
X<10
Y<10
A2
V:=1
V:=2
X:=0
Criticial Section
X>10
B1
Y:=0
B2
Y>10
V=1
V=2
CS1
CS2
AGCS1  CS 2 
Fischer’s cont.
A1
Untimed case
A2
Timed case
A1,A2,v=1
A1,A2,v=1
x=y=0
A1,A2,v=1
0 <x=y <1
X<1
Y<1
X:=0
V:=1
B1
Y:=0
V:=2
A1,A2,v=1
x=y=1
X>1
B2
Y>1
V=1
CS1
V=2
CS2
A1,A2,v=1
1 <x,y
A1,B2,v=2
A1,CS2,v=2
A1,B2,v=2
0 <x<1
y=0
B1,CS2,v=1
A1,CS2,v=2
1 <x,y
CS1,CS2,v=1
A1,B2,v=2
0 <y < x<1
A1,B2,v=2
0 <y < x=1
y=0
A1,B2,v=2
0 <y<1
1 <x
A1,B2,v=2
1 <x,y
A1,B2,v=2
y=1
1 <x
No further behaviour possible!!
Partial
Region Graph