Tag: finite state automata

NFA and DFA Equivalence Theorem Proof and Example

Finite state automata (FSA), also known as finite state machines (FSM), are usually classified as being deterministic (DFA) or non-deterministic (NFA). A deterministic finite state automaton has exactly one transition from every state for each possible input. In other words, whatever state the FSA is in, if it encounters a symbol for which a transition …

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Proof of Kleene’s Theorem

Base Regular Language Transition Graphs

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 …

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Kleene’s Theorem

Stephen Kleene

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 …

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Not String Theory – String Facts

Strings

As a computer programmer for more than a quarter of century, I don’t think I have ever thought much about strings. I knew the basics. In every language I’d worked with, strings were a data type unto themselves. Superficially they are a sequence of characters, but behind the scenes, computers store and manipulate them as …

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