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Summary: Theory of Computation
Lecture 11: Algorithms
Max Alekseyev
University of South Carolina
February 16, 2012
Algorithms
Algorithms have been around since ancient times. Informally they
can be called "procedures" or "recipies".
One of the famous algorithms was given by Euclid around 300 BC
(now called Euclid's algorithm) for finding the greatest common
divisor (GCD) of two integers.
However, there was no rigorous definition of the algorithm until the
twentieth century.
Hilbert's Tenth Problem
In 1900, at the International Congress of Mathematicians, David
Hilbert posed a list of open problems as a challenge for the coming
century. The tenth problem problem was about an algorithm.
He asked to "devise" a procedure for answering to the question
whether a given polynomial such as
6x3
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