Theory of Computation

Learn the skills and acquire the intuition to assess thetheoretical limitations of computer programming Offering an accessible approach to the topic, Theory ofComputation focuses on the metatheory of computing and thetheoretical boundaries between what various computational modelscan do and not do--from the most general model, the URM(Unbounded Register Machines), to the finite automaton. A wealth ofprogramming-like examples and easy-to-follow explanations build thegeneral theory gradually, which guides readers through the modelingand mathematical analysis of computational phenomena and providesinsights on what makes things tick and also what restrains theability of computational processes. Recognizing the importance of acquired practical experience, thebook begins with the metatheory of general purpose computerprograms, using URMs as a straightforward, technology-independentmodel of modern high-level programming languages while alsoexploring the restrictions of the URM language. Once readers gainan understanding of computability theory--including theprimitive recursive functions--the author presents automataand languages, covering the regular and context-free languages aswell as the machines that recognize these languages. Severaladvanced topics such as reducibilities, the recursion theorem,complexity theory, and Cook's theorem are also discussed. Featuresof the book include: * A review of basic discrete mathematics, covering logic andinduction while omitting specialized combinatorial topics * A thorough development of the modeling and mathematical analysisof computational phenomena, providing a solid foundation ofun-computability * The connection between un-computability and un-provability:Gödel's first incompleteness theorem The book provides numerous examples of specific URMs as well asother programming languages including Loop Programs, FA(Deterministic Finite Automata), NFA (Nondeterministic FiniteAutomata), and PDA (Pushdown Automata). Exercises at the end ofeach chapter allow readers to test their comprehension of thepresented material, and an extensive bibliography suggestsresources for further study. Assuming only a basic understanding of general computerprogramming and discrete mathematics, Theory of Computationserves as a valuable book for courses on theory of computation atthe upper-undergraduate level. The book also serves as an excellentresource for programmers and computing professionals wishing tounderstand the theoretical limitations of their craft.