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cs606 gdb
Finite automata, which are equivalent to regular expressions. Regular expressions are widely
used in programming for matching strings and extracting text. They are a simple method of
describing a set of valid strings using basic characters, grouping, and repitition. They can do a
lot, but they can't match balanced sets of parentheses.
 Push-down automata, equivalent to context-free grammars. Text/input parsers and compilers use
these when regular expressions aren't powerful enough (and one of the things you learn in
studying finite automata is what regular expressions can't do, which is crucial to knowing when
to write a regular expression and when to use something more complicated). Context-free
grammars can describe "languages" (sets of valid strings) where the validity at a certain point in
parsing the string does not depend on what else has been seen.
 Turing machines, equivalent to general computation (anything you can do with a computer).
Some of the things you learn when you cover these enable you to understand the limits of
computing itself. A good theory course will teach you about the Halting Problem, which enables
you to identify problems for which it is impossible to write a program. Once you've identified
such a problem, then you know to stop trying (or refine it to something that is possible).

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