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37 lines
1.1 KiB
37 lines
1.1 KiB
// self stabilisation algorithm Beauquier, Gradinariu and Johnen
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// gxn/dxp 18/07/02
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mdp
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// module of process 1
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module process1
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d1 : bool; // probabilistic variable
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p1 : bool; // deterministic variable
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[] d1=d7 & p1=p7 -> 0.5 : (d1'=!d1) & (p1'=p1) + 0.5 : (d1'=!d1) & (p1'=!p1);
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[] d1=d7 & !p1=p7 -> (d1'=!d1);
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endmodule
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// add further processes through renaming
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module process2 = process1 [ p1=p2, p7=p1, d1=d2, d7=d1 ] endmodule
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module process3 = process1 [ p1=p3, p7=p2, d1=d3, d7=d2 ] endmodule
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module process4 = process1 [ p1=p4, p7=p3, d1=d4, d7=d3 ] endmodule
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module process5 = process1 [ p1=p5, p7=p4, d1=d5, d7=d4 ] endmodule
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module process6 = process1 [ p1=p6, p7=p5, d1=d6, d7=d5 ] endmodule
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module process7 = process1 [ p1=p7, p7=p6, d1=d7, d7=d6 ] endmodule
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// cost - 1 in each state (expected steps)
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rewards "steps"
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true : 1;
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endrewards
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// initial states - any state with more than 1 token, that is all states
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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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formula num_tokens = (p1=p2?1:0)+(p2=p3?1:0)+(p3=p4?1:0)+(p4=p5?1:0)+(p5=p6?1:0)+(p6=p7?1:0)+(p7=p1?1:0);
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