Finite Love Machine

A finite state machine is a theoretical (and often practical) object in computer science. It has the ability to recognize certain class of patterns-- patterns that can be checked with finite amount of memory.

So given a pattern that asks you to keep track of increasing amount of information, it is impossible to construct a finite machine to recognize every instances of that pattern.

The pattern 10100100010000... is one such example, because it asks you to build a finite machine that can keep track of the increasing amount of zeroes that separate each ones.