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