DEFINATION ABOUT Automata Theory

Automata theory is a further step in abstracting your attention away from any
particular kind of computer or particular programming language. In automata theory
we consider a mathematical model of computing. Such a model strips the computational
machinery—the “programming language”—down to the bare minimum, so that it’s easy
to manipulate these theoretical machines (there are several such models, for different purposes, as you’ll soon see) mathematically to prove things about their capabilities.
For the most part, these mathematical models are not used for practical programming
problems. Real programming languages are much more convenient to use. But the very
flexibility that makes real languages easier to use also makes them harder to talk about in a formal way. The stripped-down theoretical machines are designed to be examined

mathematically.

What’s a mathematical model? You’ll see one shortly, called a “finite-state machine.”
The point of this study is that the mathematical models are, in some important ways,
to real computers and real programming languages. What this means is that
any problem that can be solved on a real computer can be solved using these models,and vice versa. Anything we can prove about the models sheds light on the real problems of computer programming as well.
The questions asked in automata theory include these: Are there any problems that
no computer can solve, no matter how much time and memory it has? Is it possible to
PROVE that a particular computer program will actually solve a particular problem? If a computer can use two different external storage devices (disks or tapes) at the same time,does that extend the range of problems it can solve compared to a machine with only one such device?
There is also a larger question lurking in the background of automata theory: Does
the human mind solve problems in the same way that a computer does? Are people
subject to the same limitations as computers? Automata theory does not actually answer this question, but the insights of automata theory can be helpful in trying to work out an answer. We’ll have more to say about this in the chapter on artificial intelligence