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

mdp

// module of process 1
module process1
	
	d1 : bool; // probabilistic variable
	p1 : bool; // deterministic variable
	
	[] d1=d3 &  p1=p3 -> 0.5 : (d1'=!d1) & (p1'=p1) + 0.5 : (d1'=!d1) & (p1'=!p1);
	[] d1=d3 & !p1=p3 -> (d1'=!d1);
	
endmodule

// add further processes through renaming
module process2 = process1 [ p1=p2, p3=p1, d1=d2, d3=d1 ] endmodule
module process3 = process1 [ p1=p3, p3=p2, d1=d3, d3=d2 ] endmodule

// cost - 1 in each state (expected steps)
rewards "steps"
	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 = (p1=p2?1:0)+(p2=p3?1:0)+(p3=p1?1:0);