An Introduction to Theory of Computation: An Algorithmic Approach by Mitsunori Ogihara

This textbook aims to provide a comprehensive introduction to the theory of computation for upper-level undergraduate students and first-year graduate students in computer science and related disciplines. It covers a wide range of foundational topics essential for understanding the principles and applications of computation. The book begins with regular languages, exploring finite automata, nondeterministic finite automata, regular expressions, and the equivalence among these apparatuses. It explores state minimization and the Myhill-Nerode Theorem, offering techniques such as pumping lemmas to identify non-regular languages and using the Myhill-Nerode Theorem for non-regularity proofs. Additionally, the closure properties of regular languages are examined. Context-free languages are another focal point, where the text discusses context-free grammars, Chomsky normal form grammars, pushdown automata, and their equivalences. The book includes pumping lemmas and closure properties using CNF grammars and PDA analysis, as well as identifying non-context-free languages and understanding leftmost derivations. Turing machine models are thoroughly covered, with various models and simulations explained. The book outlines configurations, the Church-Turing Thesis, and differentiates between recursive and recursively enumerable languages. Read more