Assume that the digital representation of a picture consists of a single number, representing a color value, for each pixel location. Let I be a picture and I be an encoding (to be clearly specified by you) of I as a string over , for = {0, 1, ; , #}. Give an implementation-level description of a Turing machine M which takes as input a string w = x;y;c##I where x N is the x-coordinate of a pixel location, y N is the y-coordinate, c N is a number representing a color, and I is an encoding of a picture. M should accept w if the pixel of I at coordinate (x, y) has color c, and should reject otherwise. (Note that the representation of I given as input must be generic and cannot have any special marking which distinguishes the pixel at location (x, y).)

Before giving the description of M, clearly specify your encoding of I as I, i.e. how the image is represented as a string over .

Your description of M should also specify how the numbers for x, y, and c are represented. (Hint: a long, i.e. non-compact, representation of numbers may make your implementation easier to define.)