There is a nice way to define randomness by determining if given a string generated by the process (i.e. 010101011110101)can you write a program smaller than th

There is a nice way to define randomness by determining if given a string generated by the process (i.e. 010101011110101)can you write a program smaller than the string that will output that string for any string generated by the process. This is called Kolmogorov randomness and has nothing to do with how input effects the output. In this instance, any string generated by a million coin tosses couldn't be reproduced by an algorithm that is smaller than the string, in general. By this metric I'd argue that the process is still random. Just because the input has an effect on the output, doesn't make the output less random. "F(x) = x + rand()" is still a random function.