I’d interpret “shortest computer program” more like ” the shortest string of ones and zeroes that gets the job done on an idealistic Turing machine” or some such. High-level programming languages are for the convenience of programmers, not computers. Thus, to use the built-in preg_match function of PHP, you’d first of all need to represent PHP’s built-in implementation of that, and also the rest of PHP, plus some environment. If you did that I think it would turn out to be longer than if you did the same in C.
This is only to be used as a way of guiding your thoughts in the right direction, a rule of thumb, rather than an actual experiment to determine between hypothesis. Among other problems, how do you know when you have found the shortest possible way of expressing something in ones and zeroes?
I’d interpret “shortest computer program” more like ” the shortest string of ones and zeroes that gets the job done on an idealistic Turing machine” or some such. High-level programming languages are for the convenience of programmers, not computers. Thus, to use the built-in preg_match function of PHP, you’d first of all need to represent PHP’s built-in implementation of that, and also the rest of PHP, plus some environment. If you did that I think it would turn out to be longer than if you did the same in C.
This is only to be used as a way of guiding your thoughts in the right direction, a rule of thumb, rather than an actual experiment to determine between hypothesis. Among other problems, how do you know when you have found the shortest possible way of expressing something in ones and zeroes?
You don’t. That’s uncomputable in the general case, and in most nontrivial special cases as well. You can, however, put upper bounds on it.
That was my point exactly.