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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
// state space (value of variable "s")
// 0 1 2 3 4
// 5 6 7
// 8 9 10
// 11 13 12
// 13 is the target
pomdp
// can observe the walls and target
observables
o
endobservables
// o=0 - observation in initial state
// o=1 - west and north walls (s0)
// o=2 - north and south ways (s1 and s3)
// o=3 - north wall (s2)
// o=4 - east and north way (s4)
// o=5 - east and west walls (s5, s6, s7, s8, s9 and s10)
// o=6 - east, west and south walls (s11 and s12)
// o=7 - the target (s13)
const double sl;
module maze
s : [-1..13];
o : [0..7];
// initialisation
[] s=-1 -> 1/13 : (s'=0) & (o'=1)
+ 1/13 : (s'=1) & (o'=2)
+ 1/13 : (s'=2) & (o'=3)
+ 1/13 : (s'=3) & (o'=2)
+ 1/13 : (s'=4) & (o'=4)
+ 1/13 : (s'=5) & (o'=5)
+ 1/13 : (s'=6) & (o'=5)
+ 1/13 : (s'=7) & (o'=5)
+ 1/13 : (s'=8) & (o'=5)
+ 1/13 : (s'=9) & (o'=5)
+ 1/13 : (s'=10) & (o'=5)
+ 1/13 : (s'=11) & (o'=6)
+ 1/13 : (s'=12) & (o'=6);
// moving around the maze
[east] s=0 -> (1-sl):(s'=1) & (o'=2) + sl:(s'=s) & (o'=o);
[west] s=0 -> (s'=0);
[north] s=0 -> (s'=0);
[south] s=0 -> (1-sl):(s'=5) & (o'=5) + sl:(s'=s) & (o'=o);
[east] s=1 -> (1-sl):(s'=2) & (o'=3) + sl:(s'=s) & (o'=o);
[west] s=1 -> (1-sl):(s'=0) & (o'=1) + sl:(s'=s) & (o'=o);
[north] s=1 -> (s'=1);
[south] s=1 -> (s'=1);
[east] s=2 -> (1-sl):(s'=3) & (o'=2) + sl:(s'=s) & (o'=o);
[west] s=2 -> (1-sl):(s'=1) & (o'=2) + sl:(s'=s) & (o'=o);
[north] s=2 -> (s'=2);
[south] s=2 -> (1-sl):(s'=6) & (o'=5) + sl:(s'=s) & (o'=o);
[east] s=3 -> (1-sl):(s'=4) & (o'=4) + sl:(s'=s) & (o'=o);
[west] s=3 -> (1-sl):(s'=2) & (o'=3) + sl:(s'=s) & (o'=o);
[north] s=3 -> (s'=3);
[south] s=3 -> (s'=3);
[east] s=4 -> (s'=4);
[west] s=4 -> (1-sl):(s'=3) & (o'=2) + sl:(s'=s) & (o'=o);
[north] s=4 -> (s'=4);
[south] s=4 -> (1-sl):(s'=7) & (o'=5) + sl:(s'=s) & (o'=o);
[east] s=5 -> (s'=5);
[west] s=5 -> (s'=5);
[north] s=5 -> (1-sl):(s'=0) & (o'=1) + sl:(s'=s) & (o'=o);
[south] s=5 -> (1-sl):(s'=8) + sl:(s'=s) & (o'=o);
[east] s=6 -> (s'=6);
[west] s=6 -> (s'=6);
[north] s=6 -> (1-sl):(s'=2) & (o'=3) + sl:(s'=s) & (o'=o);
[south] s=6 -> (1-sl):(s'=9) + sl:(s'=s) & (o'=o);
[east] s=7 -> (s'=7);
[west] s=7 -> (s'=7);
[north] s=7 -> (1-sl):(s'=4) & (o'=4) + sl:(s'=s) & (o'=o);
[south] s=7 -> (1-sl):(s'=10) + sl:(s'=s) & (o'=o);
[east] s=8 -> (s'=8);
[west] s=8 -> (s'=8);
[north] s=8 -> (1-sl):(s'=5) + sl:(s'=s) & (o'=o);
[south] s=8 -> (1-sl):(s'=11) & (o'=6) + sl:(s'=s) & (o'=o);
[east] s=9 -> (s'=9);
[west] s=9 -> (s'=9);
[north] s=9 -> (1-sl):(s'=6) + sl:(s'=s) & (o'=o);
[south] s=9 -> (1-sl):(s'=13) & (o'=7) + sl:(s'=s) & (o'=o);
[east] s=10 -> (s'=10);
[west] s=10 -> (s'=10);
[north] s=10 -> (1-sl):(s'=7) + sl:(s'=s) & (o'=o);
[south] s=10 -> (1-sl):(s'=12) & (o'=6) + sl:(s'=s) & (o'=o);
[east] s=11 -> (s'=11);
[west] s=11 -> (s'=11);
[north] s=11 -> (1-sl):(s'=8) & (o'=5) + sl:(s'=s) & (o'=o);
[south] s=11 -> (s'=11);
[east] s=12 -> (s'=12);
[west] s=12 -> (s'=12);
[north] s=12 -> (1-sl):(s'=10) & (o'=5) + sl:(s'=s) & (o'=o);
[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)/7
rewards
[east] true : 1/7;
[west] true : 1/7;
[north] true : 1/7;
[south] true : 1/7;
endrewards
// target observation
label "goal" = o=7;
label "bad" = o=6;