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Good Math by Mark C. Chu-Carroll

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21Finite State Machines: Simplicity Goes Far

When mathematicians and computer scientists try to describe computation, we start with very simple machines and then gradually add capabilities, creating different kinds of machines that have different limits until we get to the most complex machines that can be built.

We’re not going to go through all of the possible classes of computing devices—that would take a much longer book than this one! Instead, we’ll look at the two types of machines that form the limits: the most limited simple machines and the most powerful complex ones.

We’ll start looking at computing by looking at the simplest kind of computing machine that does anything useful. This type of machine is called a finite state machine ...

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