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// Example 2 from
// "Verification and Control of Partially Observable Probabilistic Real-Time Systems"
// Norman/Parker/Zou, FORMATS 2015
// Or Example 4 from
// "Verification and Control of Partially Observable Probabilistic Systems"
// Norman/Parker/Zou, Real-Time Systems, 53(3), 2017
popta
observables x, o endobservables
module M
x : clock;
l : [0..3] init 0;
o : [0..2] init 0; // 0, 1&2, 3
invariant
(l=0 => x<=1) &
(l=1 => x<=2) &
(l=2 => x<=2) &
(l=3 => true)
endinvariant
[a0] l=0 & x<=1 -> 1/2 : (l'=1)&(o'=1) + 1/2 : (l'=2)&(o'=1)&(x'=0);
[a1] l=1 & x<=2 -> (l'=3)&(o'=2);
[a2] l=1 & x<=2 -> (l'=3)&(o'=2);
[a1] l=2 & x<=2 -> (l'=3)&(o'=2);
[a2] l=2 & x<=2 -> (l'=3)&(o'=2);
endmodule
label "goal" = o=2;
rewards
[a2] l=1 : 1;
[a1] l=2 : 1;
l=0 : 1;
endrewards