Yeah, the first test of finite state machinery on the human mind was done at Bell Labs by an engineer whose name I forget off the top of my head. The thing was, I believe it was originally done as a lark (you can pull minor "impossible" feats with it for fun and profit). The significance wasn't identified until much later. By "test", there are mathematical tests that can detect "finite state machine-ness". The relevant conditions and caveats can be found with the theory; it needs to be understood to really grasp the capabilities and limitations. You can't prove that something is a finite state machine; the best you can hope for is to demonstrate ad infinitum that it can't behave as anything BUT a finite state machine.
Ironic isn't it? This is exactly the path being followed by ID theorists.