You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
62 lines
1.8 KiB
62 lines
1.8 KiB
// N-processor mutual exclusion [Rab82]
|
|
// with global variables to remove sychronization
|
|
// gxn/dxp 02/02/00
|
|
|
|
nondeterministic
|
|
|
|
// size of shared counter
|
|
const int K = 6; // 4+ceil(log_2 N)
|
|
|
|
// global variables (all modules can read and write)
|
|
// c=0 critical section free
|
|
// c=1 critical section not free
|
|
// b current highest draw
|
|
// r current round
|
|
|
|
global c : [0..1];
|
|
global b : [0..K];
|
|
global r : [1..2];
|
|
|
|
// local variables: process i
|
|
// state: pi
|
|
// 0 remainder
|
|
// 1 trying
|
|
// 2 critical section
|
|
// current draw: bi
|
|
// current round: ri
|
|
|
|
// atomic formula for process 1 drawing
|
|
formula draw = p1=1 & (b<b1 | r!=r1);
|
|
|
|
module process1
|
|
|
|
p1 : [0..2];
|
|
b1 : [0..K];
|
|
r1 : [0..2];
|
|
|
|
// remain in remainder
|
|
[] p1=0 -> (p1'=0);
|
|
// enter trying
|
|
[] p1=0 -> (p1'=1);
|
|
// make a draw
|
|
[] draw -> 0.5 : (b1'=1) & (r1'=r) & (b'=max(b,1))
|
|
+ 0.25 : (b1'=2) & (r1'=r) & (b'=max(b,2))
|
|
+ 0.125 : (b1'=3) & (r1'=r) & (b'=max(b,3))
|
|
+ 0.0625 : (b1'=4) & (r1'=r) & (b'=max(b,4))
|
|
+ 0.03125 : (b1'=5) & (r1'=r) & (b'=max(b,5))
|
|
+ 0.03125 : (b1'=6) & (r1'=r) & (b'=max(b,6));
|
|
// enter critical section and randomly set r to 1 or 2
|
|
[] p1=1 & b=b1 & r=r1 & c=0 -> 0.5 : (r'=1) & (c'=1) & (b'=0) & (b1'=0) & (r1'=0) & (p1'=2)
|
|
+ 0.5 : (r'=2) & (c'=1) & (b'=0) & (b1'=0) & (r1'=0) & (p1'=2);
|
|
// loop when trying and cannot make a draw or enter critical section
|
|
[] p1=1 & r1=r & b1<=b & ((c=0 & b1!=b) | c=1) -> (p1'=p1);
|
|
// leave crictical section
|
|
[] p1=2 -> (p1'=0) & (c'=0);
|
|
// stay in critical section
|
|
[] p1=2 -> (p1'=2);
|
|
|
|
endmodule
|
|
|
|
// construct further modules through renaming
|
|
module process2 = process1 [p1=p2, b1=b2, r1=r2] endmodule
|
|
module process3 = process1 [p1=p3, b1=b3, r1=r3] endmodule
|