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48 lines
1.5 KiB
48 lines
1.5 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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const double p = 0.5;
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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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[step] (x1=x11) -> p : (x1'=0) + 1-p : (x1'=1);
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[step] !(x1=x11) -> (x1'=x11);
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endmodule
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// add further processes through renaming
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module process2 = process1 [ x1=x2, x11=x1 ] endmodule
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module process3 = process1 [ x1=x3, x11=x2 ] endmodule
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module process4 = process1 [ x1=x4, x11=x3 ] endmodule
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module process5 = process1 [ x1=x5, x11=x4 ] endmodule
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module process6 = process1 [ x1=x6, x11=x5 ] endmodule
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module process7 = process1 [ x1=x7, x11=x6 ] endmodule
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module process8 = process1 [ x1=x8, x11=x7 ] endmodule
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module process9 = process1 [ x1=x9, x11=x8 ] endmodule
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module process10 = process1 [ x1=x10, x11=x9 ] endmodule
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module process11 = process1 [ x1=x11, x11=x10 ] endmodule
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// cost - 1 in each state (expected number of steps)
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rewards "steps"
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true : 1;
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endrewards
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// set of initial states: all (i.e. any possible initial configuration of tokens)
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init
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true
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endinit
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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=x2?1:0)+(x2=x3?1:0)+(x3=x4?1:0)+(x4=x5?1:0)+(x5=x6?1:0)+(x6=x7?1:0)+(x7=x8?1:0)+(x8=x9?1:0)+(x9=x10?1:0)+(x10=x11?1:0)+(x11=x1?1:0);
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// label - stable configurations (1 token)
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label "stable" = num_tokens=1;
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