// self stabilisation algorithm Beauquier, Gradinariu and Johnen
// gxn/dxp 18/07/02

// model is an mdp
nondeterministic

// module of process 1
module process1
	
	d1 : bool; // probabilistic variable
	p1 : bool; // deterministic variable
	
	[] (d1=d9) &  (p1=p9) -> 0.5 : (d1'=!d1) & (p1'=p1) + 0.5 : (d1'=!d1) & (p1'=!p1);
	[] (d1=d9) & !(p1=p9) -> (d1'=!d1);
	
endmodule

// add further processes through renaming
module process2 =process1[p1=p2 ,p9=p1, d1=d2 ,d9=d1] endmodule
module process3 =process1[p1=p3 ,p9=p2, d1=d3 ,d9=d2] endmodule
module process4 =process1[p1=p4 ,p9=p3, d1=d4 ,d9=d3] endmodule
module process5 =process1[p1=p5 ,p9=p4, d1=d5 ,d9=d4] endmodule
module process6 =process1[p1=p6 ,p9=p5, d1=d6 ,d9=d5] endmodule
module process7 =process1[p1=p7 ,p9=p6, d1=d7 ,d9=d6] endmodule
module process8 =process1[p1=p8 ,p9=p7, d1=d8 ,d9=d7] endmodule
module process9 =process1[p1=p9 ,p9=p8, d1=d9 ,d9=d8] endmodule

// cost - 1 in each state (expected steps)
rewards
	true : 1;
endrewards

// initial states - any state with more than 1 token, that is all states
init
	true
endinit

// formula, for use in properties: number of tokens
formula num_tokens = (p9=p1?1:0)+(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=p8?1:0)+(p8=p9?1:0);