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Computability refers to the study of the mathematical foundations of computation: what is an appropriate mathematical model of a computer, what types of computations are possible in the model, what types are not, the inherent complexity of certain computations and so forth. Perhaps surprisingly, many concepts from the theory of computation have become of fundamental importance in other areas of computer science, such as computational linguistics, compiler design, hardware design, objectoriented design, artificial intelligence, and even the syntax of the UNIX grep and awk commands.
In this course we will investigate the interaction between various models of computation. Along the way the intimate connection between computation and language recognition will be developed. We will study several classes of abstract machine including finite automata, pushdown automata and Turing machines along with several classes of languages such as regular and contextfree languages. In addition we will examine some of those problems, such as the Halting Problem, which are not amenable to computer solution.
We will also investigate the use of formal logics in computer science, defining a variety of logics and examining their strengths and weaknesses in expressiveness and the difficulty of creating proofs. We will examir logics that are particularly useful in proving programs (in both software and hardware) correct.
By the end of this course, you should be able to: