{"product_id":"an-introduction-to-theory-of-computation-an-algorithmic-approach-9783031847424","title":"An Introduction to Theory of Computation: An Algorithmic Approach","description":"\u003cp\u003e • Author(s): Mitsunori Ogihara\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: Computer Science\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis 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.\u003c\/p\u003e \u003cp\u003eThe 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.\u003c\/p\u003e \u003cp\u003eContext-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.\u003c\/p\u003e \u003cp\u003eTuring 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.\u003c\/p\u003e \u003cp\u003eDecidability and undecidability are critical topics in the text, addressing decidable problems, diagonalization, the halting problem, and Rice's Theorem. It also provides a characterization of decidability, discusses the Post Correspondence Problem, and examines the lower levels of the arithmetical hierarchy.\u003c\/p\u003e \u003cp\u003eThe textbook also delves into computational complexity classes, defining time and space complexity classes, and presenting efficient simulations and hierarchy theorems, including the Hennie-Stearns Theorem. It includes examples of problems in P and NP, providing a clear understanding of these classifications.\u003c\/p\u003e \u003cp\u003eNP-completeness is explored in detail, covering SAT and 3SAT, canonical complete problems, and various NP-complete problems. The book extends to space complexity classes, discussing PSPACE complete problems, NL-complete problems, and proving that NL=coNL.\u003c\/p\u003e \u003cp\u003eFinally, the text ventures beyond NP-completeness, discussing Ladner's construction of non-NPC sets, randomized complexity classes, and concepts such as BPP and the polynomial hierarchy. It also examines polynomial size circuits, providing a comprehensive view of the landscape of computational complexity.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Paperback","offer_id":47854047264919,"sku":"9783031847424","price":4804.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9783031847424.webp?v=1780038462","url":"https:\/\/atlanticbooks.com\/products\/an-introduction-to-theory-of-computation-an-algorithmic-approach-9783031847424","provider":"Atlantic Books","version":"1.0","type":"link"}