// randomized dining philosophers [LR81]
// dxp/gxn 23/01/02

// model which does not require fairness
// remove the possibility of loops:
// (1) cannot stay in thinking 
// (2) if first fork not free then cannot move (another philosopher must more)

mdp

// atomic formulae 
// left fork free and right fork free resp.
formula lfree = (p2>=0&p2<=4)|p2=6|p2=10;
formula rfree = (p10>=0&p10<=3)|p10=5|p10=7|p10=11;

module phil1

	p1: [0..11];

	[] p1=0 -> (p1'=1); // trying
	[] p1=1 -> 0.5 : (p1'=2) + 0.5 : (p1'=3); // draw randomly
	[] p1=2 &  lfree -> (p1'=4); // pick up left
	[] p1=3 &  rfree -> (p1'=5); // pick up right
	[] p1=4 &  rfree -> (p1'=8); // pick up right (got left)
	[] p1=4 & !rfree -> (p1'=6); // right not free (got left)
	[] p1=5 &  lfree -> (p1'=8); // pick up left (got right)
	[] p1=5 & !lfree -> (p1'=7); // left not free (got right)
	[] p1=6  -> (p1'=1); // put down left
	[] p1=7  -> (p1'=1); // put down right
	[] p1=8  -> (p1'=9); // move to eating (got forks)
	[] p1=9  -> (p1'=10); // finished eating and put down left 
	[] p1=9  -> (p1'=11); // finished eating and put down right
	[] p1=10 -> (p1'=0); // put down right and return to think
	[] p1=11 -> (p1'=0); // put down left and return to think

endmodule

// construct further modules through renaming
module phil2 = phil1 [ p1=p2, p2=p3, p10=p1 ] endmodule
module phil3 = phil1 [ p1=p3, p2=p4, p10=p2 ] endmodule
module phil4 = phil1 [ p1=p4, p2=p5, p10=p3 ] endmodule
module phil5 = phil1 [ p1=p5, p2=p6, p10=p4 ] endmodule
module phil6 = phil1 [ p1=p6, p2=p7, p10=p5 ] endmodule
module phil7 = phil1 [ p1=p7, p2=p8, p10=p6 ] endmodule
module phil8 = phil1 [ p1=p8, p2=p9, p10=p7 ] endmodule
module phil9 = phil1 [ p1=p9, p2=p10, p10=p8 ] endmodule
module phil10 = phil1 [ p1=p10, p2=p1, p10=p9 ] endmodule

// rewards (number of steps)
rewards "num_steps"
	[] true : 1;
endrewards
// labels
label "hungry" = ((p1>0)&(p1<8))|((p2>0)&(p2<8))|((p3>0)&(p3<8))|((p4>0)&(p4<8))|((p5>0)&(p5<8))|((p6>0)&(p6<8))|((p7>0)&(p7<8))|((p8>0)&(p8<8))|((p9>0)&(p9<8))|((p10>0)&(p10<8));
label "eat" = ((p1>=8)&(p1<=9))|((p2>=8)&(p2<=9))|((p3>=8)&(p3<=9))|((p4>=8)&(p4<=9))|((p5>=8)&(p5<=9))|((p6>=8)&(p6<=9))|((p7>=8)&(p7<=9))|((p8>=8)&(p8<=9))|((p9>=8)&(p9<=9))|((p10>=8)&(p10<=9));