// 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