One of the annoying things that old school Artificial Intelligence researchers have to deal with is the fact that simple brute force is such a daunting foe. Back in the dawn era of the field, attempts to replicate human thought processes used deductive reasoning, symbolic representation, and incremental learning to solve problems. As an example, [...]

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Not understanding some basic rules of mathematics or logic can be a problem if you are a computer programmer. It can stand in the way of a good solution to a problem, or worse yet, can cause you to spend a lot of time working on a dead end. In the case of New Zealand [...]

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You may have never heard of Vinay Deolalikar, but there is a chance that he may become next year’s Turing Award winner, not to mention an overnight millionaire. It seems that Vinay dropped the news at the start of this week that he had proven that P does not equal NP. In short, this proof [...]

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Back in 1981, fresh out of school, I was awestruck by Steve Wozniak’s program that calculated over 100,000 digits of e on an Apple II. (Anyone who has a scan of his article in the June 1981 issue of Byte, please email me a copy!) Shortly after reading the article, I ported his program to [...]

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The Pigeonhole Principle, also referred to as the Counting Theorem, is a handy tool for mathematicians, and naturally, computer programmers. The loose version of this principle says “After placing n pigeons into m compartments, if n is greater than m, you will find that some compartment must contain more than one pigeon.” Seems obvious, and [...]

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