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// PRISM Model of a simple robot game // - A player - friendlyRobot - moves around and tries not to "crash" with another player - adversary Robot. // - friendlyRobot can choose the direction of movement. // - adversaryRobot should move in a circle counterclockwise on the grid, but has a probabilty to fail and move into the wrong direction. // - The movement of adversaryRobot is defined as a pseudo random movement with probabilty = 1/4 into one of the 4 possible directions.
smg
player friendlyRobot [e1], [w1], [n1], [s1] endplayer
player adversaryRobot [e2], [w2], [n2], [s2], [middle] endplayer
// 3x3 grid const int width = 2; const int height = 2;
const int xmin = 0; const int xmax = width; const int ymin = 0; const int ymax = height;
// probabilty to fail const double failProb = 1/10; const double notFailProb = 1-failProb;
// definition of randomProb, this has to be 0.25 since it is the prob of go into one direction from the middle for the adverseryRobot const double randomProb = 1/4;
global move : [0..1] init 0;
//F__ //___ //__R
label "crash" = x1=x2 & y1=y2;
module robot1 x1 : [0..width] init 0; y1 : [0..height] init 0;
[e1] move=0 & x1<xmax -> (x1'=x1+1) & (move'=1); [w1] move=0 & x1>0 -> (x1'=x1-1) & (move'=1); [n1] move=0 & y1>0 -> (y1'=y1-1) & (move'=1); [s1] move=0 & y1<ymax -> (y1'=y1+1) & (move'=1); endmodule
module robot2 x2 : [0..width] init width; y2 : [0..height] init height;
[e2] move=1 & x2<xmax & y2=ymax -> notFailProb : (x2'=x2+1) & (move'=0) + failProb : (y2'=y2-1) & (move'=0); [w2] move=1 & x2>0 & y2=0 -> notFailProb : (x2'=x2-1) & (move'=0) + failProb : (y2'=y2+1) & (move'=0); [n2] move=1 & x2=xmax & y2>0 -> notFailProb : (y2'=y2-1) & (move'=0) + failProb : (x2'=x2-1) & (move'=0); [s2] move=1 & x2=0 & y2<ymax -> notFailProb : (y2'=y2+1) & (move'=0) + failProb : (x2'=x2+1) & (move'=0);
[middle] move=1 & x2=1 & y2=1 -> randomProb : (x2'=x2+1) & (move'=0) + randomProb : (x2'=x2-1) & (move'=0) + randomProb : (y2'=y2-1) & (move'=0) + randomProb : (y2'=y2+1) & (move'=0); endmodule
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