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46 lines
1.3 KiB
46 lines
1.3 KiB
// herman's self stabilising algorithm [Her90]
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// gxn/dxp 13/07/02
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// the procotol is synchronous with no nondeterminism (a DTMC)
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dtmc
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// coin
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const double p;
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// module for process 1
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module process1
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// Boolean variable for process 1
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x1 : [0..1];
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i1 : bool init false;
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[initial] (!i1) -> 0.5 : (x1'=0) & (i1'=true) + 0.5 : (x1'=1) & (i1'=true);
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[step] (i1 & x1=x0) -> p : (x1'=0) + 1-p : (x1'=1);
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[step] (i1 & x1!=x0) -> (x1'=x0);
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endmodule
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// add further processes through renaming
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module process2 = process1 [ x1=x2, x0=x1, i1=i2 ] endmodule
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module process3 = process1 [ x1=x3, x0=x2, i1=i3 ] endmodule
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module process4 = process1 [ x1=x4, x0=x3, i1=i4 ] endmodule
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module process5 = process1 [ x1=x0, x0=x4, i1=i5 ] endmodule
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formula initialized = i1 & i2 & i3 & i4 & i5;
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// cost - 1 in each state (expected number of steps)
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rewards "steps"
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initialized : 1;
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endrewards
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// formula, for use in properties: number of tokens
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// (i.e. number of processes that have the same value as the process to their left)
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formula num_tokens = (x1=x0?1:0)
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+(x2=x1?1:0)
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+(x3=x2?1:0)
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+(x4=x3?1:0)
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+(x0=x4?1:0);
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// label - stable configurations (1 token)
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label "stable" = num_tokens=1 & initialized;
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