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// maze example (POMDP)
// slightly extends that presented in
// Littman, Cassandra and Kaelbling
// Learning policies for partially observable environments: Scaling up
// Technical Report CS, Brown University
// gxn 29/01/16
// Made into a MDP for documentation of stormpy.
// state space (value of variable "s")
// 0 1 2 3 4
// 5 6 7
// 8 9 10
// 11 13 12
// 13 is the target
mdp
module maze
s : [-1..13];
// initialisation
[] s=-1 -> 1/13 : (s'=0)
+ 1/13 : (s'=1)
+ 1/13 : (s'=2)
+ 1/13 : (s'=3)
+ 1/13 : (s'=4)
+ 1/13 : (s'=5)
+ 1/13 : (s'=6)
+ 1/13 : (s'=7)
+ 1/13 : (s'=8)
+ 1/13 : (s'=9)
+ 1/13 : (s'=10)
+ 1/13 : (s'=11)
+ 1/13 : (s'=12);
// moving around the maze
[east] s=0 -> (s'=1);
[west] s=0 -> (s'=0);
[north] s=0 -> (s'=0);
[south] s=0 -> (s'=5);
[east] s=1 -> (s'=2);
[west] s=1 -> (s'=0);
[north] s=1 -> (s'=1);
[south] s=1 -> (s'=1);
[east] s=2 -> (s'=3);
[west] s=2 -> (s'=1);
[north] s=2 -> (s'=2);
[south] s=2 -> (s'=6);
[east] s=3 -> (s'=4);
[west] s=3 -> (s'=2);
[north] s=3 -> (s'=3);
[south] s=3 -> (s'=3);
[east] s=4 -> (s'=4);
[west] s=4 -> (s'=3);
[north] s=4 -> (s'=4);
[south] s=4 -> (s'=7);
[east] s=5 -> (s'=5);
[west] s=5 -> (s'=5);
[north] s=5 -> (s'=0);
[south] s=5 -> (s'=8);
[east] s=6 -> (s'=6);
[west] s=6 -> (s'=6);
[north] s=6 -> (s'=2);
[south] s=6 -> (s'=9);
[east] s=7 -> (s'=7);
[west] s=7 -> (s'=7);
[north] s=7 -> (s'=4);
[south] s=7 -> (s'=10);
[east] s=8 -> (s'=8);
[west] s=8 -> (s'=8);
[north] s=8 -> (s'=5);
[south] s=8 -> (s'=11);
[east] s=9 -> (s'=9);
[west] s=9 -> (s'=9);
[north] s=9 -> (s'=6);
[south] s=9 -> (s'=13);
[east] s=10 -> (s'=10);
[west] s=10 -> (s'=10);
[north] s=10 -> (s'=7);
[south] s=10 -> (s'=12);
[east] s=11 -> (s'=11);
[west] s=11 -> (s'=11);
[north] s=11 -> (s'=8);
[south] s=11 -> (s'=11);
[east] s=12 -> (s'=12);
[west] s=12 -> (s'=12);
[north] s=12 -> (s'=10);
[south] s=12 -> (s'=12);
// loop when we reach the target
[done] s=13 -> true;
endmodule
// reward structure (number of steps to reach the target)
rewards
[east] true : 1;
[west] true : 1;
[north] true : 1;
[south] true : 1;
endrewards
// target observation
label "goal" = s=13;