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.
89 lines
2.6 KiB
89 lines
2.6 KiB
// synchronous leader election protocol (itai & Rodeh)
|
|
// dxp/gxn 25/01/01
|
|
|
|
dtmc
|
|
|
|
// CONSTANTS
|
|
const int N = 5; // number of processes
|
|
const int K = 8; // range of probabilistic choice
|
|
|
|
// counter module used to count the number of processes that have been read
|
|
// and to know when a process has decided
|
|
module counter
|
|
|
|
// counter (c=i means process j reading process (i-1)+j next)
|
|
c : [1..N-1];
|
|
|
|
// reading
|
|
[read] c<N-1 -> (c'=c+1);
|
|
// finished reading
|
|
[read] c=N-1 -> (c'=c);
|
|
//decide
|
|
[done] u1|u2|u3|u4|u5 -> (c'=c);
|
|
// pick again reset counter
|
|
[retry] !(u1|u2|u3|u4|u5) -> (c'=1);
|
|
// loop (when finished to avoid deadlocks)
|
|
[loop] s1=3 -> (c'=c);
|
|
|
|
endmodule
|
|
|
|
// processes form a ring and suppose:
|
|
// process 1 reads process 2
|
|
// process 2 reads process 3
|
|
// process 3 reads process 1
|
|
module process1
|
|
|
|
// local state
|
|
s1 : [0..3];
|
|
// s1=0 make random choice
|
|
// s1=1 reading
|
|
// s1=2 deciding
|
|
// s1=3 finished
|
|
|
|
// has a unique id so far (initially true)
|
|
u1 : bool;
|
|
|
|
// value to be sent to next process in the ring (initially sets this to its own value)
|
|
v1 : [0..K-1];
|
|
|
|
// random choice
|
|
p1 : [0..K-1];
|
|
|
|
// pick value
|
|
[pick] s1=0 -> 1/K : (s1'=1) & (p1'=0) & (v1'=0) & (u1'=true)
|
|
+ 1/K : (s1'=1) & (p1'=1) & (v1'=1) & (u1'=true)
|
|
+ 1/K : (s1'=1) & (p1'=2) & (v1'=2) & (u1'=true)
|
|
+ 1/K : (s1'=1) & (p1'=3) & (v1'=3) & (u1'=true)
|
|
+ 1/K : (s1'=1) & (p1'=4) & (v1'=4) & (u1'=true)
|
|
+ 1/K : (s1'=1) & (p1'=5) & (v1'=5) & (u1'=true)
|
|
+ 1/K : (s1'=1) & (p1'=6) & (v1'=6) & (u1'=true)
|
|
+ 1/K : (s1'=1) & (p1'=7) & (v1'=7) & (u1'=true);
|
|
// read
|
|
[read] s1=1 & u1 & c<N-1 -> (u1'=(p1!=v2)) & (v1'=v2);
|
|
[read] s1=1 & !u1 & c<N-1 -> (u1'=false) & (v1'=v2) & (p1'=0);
|
|
// read and move to decide
|
|
[read] s1=1 & u1 & c=N-1 -> (s1'=2) & (u1'=(p1!=v2)) & (v1'=0) & (p1'=0);
|
|
[read] s1=1 & !u1 & c=N-1 -> (s1'=2) & (u1'=false) & (v1'=0);
|
|
// deciding
|
|
// done
|
|
[done] s1=2 -> (s1'=3) & (u1'=false) & (v1'=0) & (p1'=0);
|
|
//retry
|
|
[retry] s1=2 -> (s1'=0) & (u1'=false) & (v1'=0) & (p1'=0);
|
|
// loop (when finished to avoid deadlocks)
|
|
[loop] s1=3 -> (s1'=3);
|
|
|
|
endmodule
|
|
|
|
// construct remaining processes through renaming
|
|
module process2 = process1 [ s1=s2,p1=p2,v1=v2,u1=u2,v2=v3 ] endmodule
|
|
module process3 = process1 [ s1=s3,p1=p3,v1=v3,u1=u3,v2=v4 ] endmodule
|
|
module process4 = process1 [ s1=s4,p1=p4,v1=v4,u1=u4,v2=v5 ] endmodule
|
|
module process5 = process1 [ s1=s5,p1=p5,v1=v5,u1=u5,v2=v1 ] endmodule
|
|
|
|
// expected number of rounds
|
|
rewards "num_rounds"
|
|
[pick] true : 1;
|
|
endrewards
|
|
|
|
// labels
|
|
label "elected" = s1=3&s2=3&s3=3&s4=3&s5=3;
|