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After a few computer science courses, students may start to
get the feeling that programs can always be written to
solve any computational problem. Writing the program may
be hard work. For example, it may involve learning a
difficult technique. And many hours of debugging. But
with enough time and effort, the program can be written.
So it may come as a surprise that this is not the case:
there are computational problems for which no program
exists. And these are not ill-defined problems (Can a
computer fall in love?) or uninteresting toy problems.
These are precisely defined problems with important
practical applications.
Theoretical computer science can be briefly described as
the mathematical study of computation. These notes will
introduce you to this branch of computer science by
focusing on computability theory and automata theory. You
will learn how to precisely define what computation is and
why certain computational problems cannot be solved. You
will also learn several concepts and techniques that have
important applications. Chapter 1 provides a more detailed
introduction to this rich and beautiful area of computer
science.
These notes were written for the course CS345 Automata
Theory and Formal Languages taught at Clarkson University.
The course is also listed as MA345 and CS541. The
prerequisites are CS142 (a second course in programming)
and MA211 (a course on discrete mathematics in which
students also gain experience writing mathematical proofs).