Nov 26 2017
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 …
Nov 21 2017
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
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 …
Nov 09 2017
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 …
Nov 07 2017
If you want to get your hands on a LEGO Star Wars Advent Calendar, you need to buy it in early November. That is a lesson I learned the hard way last year. The downside of planning ahead is that once you’ve got it, it will be several weeks before you can tear into day …
Oct 12 2017
Boolean functions, sometimes also called switching functions, are functions that take as their input zero or more boolean values (1 or 0, true or false, etc.) and output a single boolean value. The number of inputs to the function is is called the arity of the function and is denoted as k. Every k-ary function …
Sep 27 2017
From Vienna Bienalle 2017, taking place this week in Austria, comes a new take on Isaac Asimov’s Three Laws of Robotics. The head of the project, Christoph Thun-Hohenstein, says the update was necessitated by: …the need for benign intelligent robots and the necessity of cultivating a culture of quality committed to serving the common good! …
Sep 21 2017
If you are an artist, photographer, graphic designer, or web developer, having a firm understanding of colors is a necessity. Key to being able to study and discuss colors is a formal framework for quantizing their properties. Abstract mathematical models called color models do just this, allowing people to discuss the qualities of a color …
Jul 16 2017
An arithmetic sequence of numbers, sometimes alternatively called an arithmetic progression, is a sequence of numbers in which the difference between all pairs of consecutive numbers is constant. A very simple arithmetic sequence consists of the natural numbers: 1, 2, 3, 4, … where the difference between any number and the number before it is …
