wildeye

You can take a look at our software and test it out for yourself!

Yes, but isn't it in the literature? Minsky and Papert's seminal Perceptrons changed the face of research in the field by proving that e.g. XOR could not be implemented with a 2-layer net.

Sure, "difficult vs. easy to implement" isn't as dramatic, but it's still central enough that I would have thought that there would be a large body of formal results on the topic.

Not that you likely expected an answer, but it's computational theory from computer science.

Chomsky created modern theoretical linguistics when he showed that mathematical grammars are equivalent to computation, and that there was a hierarchy of 4 kinds, increasing in power.

A "grammar" here isn't merely the kind of nitpicking of English they teach early on in school, it just means a description of a language. For instance, ADJECTIVE NOUN is a grammar for a language that allows things like "ugly building" or "old book", but nothing else.

Regular expressions are more or less the simplest kind of mathematical grammar, and he proved that they can only compute certain simple things.

The most powerful (unrestricted) grammars, on the other hand, can compute "anything" -- they are equivalent in power to what Turing machines can do.

Turing machines are a mathematical model of computers by Alan Turing (early pioneer of computer science) that, roughly speaking, can do anything that a real world computer can do.

Philipwhiuk was commenting on the well-known (in computer science) fact that regular expressions are not powerful enough to match nested pairs of things such as parenthesis -- or HTML start/end pairs.

Not that I expect you to care much one way or the other. :)

Regex in an infinite loop is equivalent to an unrestricted grammar.

But stripping HTML doesn't require Turing equivalence. The open/close pairs don't need to be stripped in matched pairs.

You make an excellent case for dictatorship.