There are two versions of the Pumping Lemma. One is for context free grammars and one is for regular languages. This post is about the latter. The Pumping Lemma describes a property that all natural languages share. While it cannot be used by itself to prove that any given language is regular, it can be …

# Tag: kleene’s theorem

Nov 21 2017

## Proof of Kleene’s Theorem

In my last post, “Kleene’s Theorem,” I provided some useful background information about strings, regular languages, regular expressions, and finite automata before introducing the eponymously named theorem that has become one of the cornerstones of artificial intelligence and more specifically, natural language processing (NLP). Kleene’s Theorem tells us that regular expressions and finite state automata …

Nov 17 2017

## Kleene’s Theorem

Stephen Cole Kleene was an American mathematician who’s groundbreaking work in the sub-field of logic known as recursion theory laid the groundwork for modern computing. While most computer programmers might not know his name or the significance of his work regarding computable functions, I am willing to bet that anyone who has ever dealt with …