Theory of Computation by Frank Stephan

Theory of Computation by Frank Stephan

Frank Stephan's detailed lecture notes on the theory of computation cover quite a wide spectrum of issues. The document starts with the basics of sets and regular expressions, then goes ahead to grammars and the Chomsky hierarchy, helping one in understanding the structure of languages. Then it discusses finite automaton and nondeterministic finite automata, giving all details about the processing of strings by these models. The notes also treat the composition of languages, normal forms, and algorithms used in computation. Membership testing, whether deterministic or nondeterministic, is also explained, together with the proof of how models of computation handle language recognition. Finally, the approach is important when considering complexity, the problems that turn out undecidable, showing thus the intrinsic limits of computation. This is an important resource concerning formal languages, automata theory, and basic bounds of computability.

Author(s): Frank Stephan

176 Pages

Lecture Notes Theory of Computation

This lecture note from S R Engineering College offers a detailed introduction to key concepts in the Theory of Computation. It begins with Properties of Binary Operations, exploring fundamental mathematical operations and their essential properties like associativity and commutativity. The section on Concatenation Properties covers how strings can be joined and the characteristics of such operations, including associativity and the identity element. Finite Automata are thoroughly discussed, explaining both deterministic and nondeterministic (NFA) models, and their role in recognizing regular languages. The notes also cover Formal Languages, categorizing them into regular, context-free, context-sensitive, and recursively enumerable types based on complexity. Finally, the Pumping Lemma is introduced as a critical tool for proving the non-regularity and non-context-freeness of languages by demonstrating how strings in these languages can be decomposed and manipulated.

Author(s): S R Engineering College

155 Pages

Introduction to Theory of Computation by Wikiversity

This is an all-inclusive course on computational theory provided in this online resource by Wikiversity. It begins with Finite State Machines–their definitions, operations, and minimization techniques. The notes also cover closure and nondeterminism—how these properties may affect computational models. Their discussion greatly involves the Pumping Lemma, proving language property. The book also surveys Context-Free Languages and their connection to Compilers and introduces Pushdown Machines emphatically and focuses on their importance in parsing. It contains important material on the CYK algorithm for parsing and the more basic problems of Undecidability. It also surveys Turing Machines, the Halting Problem, and more general areas of Complexity Theory, including Quantified Boolean Formulae, Savitch's Theorem, and Space Hierarchy. The notes end with the Recursion Theorem, and it can be considered as a landmark in the theoretical study of the science of computers.

Author(s): Wikiversity

NA Pages

Introduction to Computational Theory Lecture Notes

These broad-ranging notes introduce some of the fundamental concepts in the theory of computation. The set starts with a brief introduction to formal languages and their classification, including regular languages and sets. In these notes, finite automata are introduced, discussing their structure and role in recognizing regular languages. This is followed by Context-Free Grammars and Pushdown Automata, focusing on the role in defining and recognizing context-free languages. This will cover Turing Machines, the original model of computation; a review of the Chomsky Hierarchy from a perspective on the various levels of languages about their power of generation. The conclusion deals with an overview of Complexity Theory, mainly dealing with the P and NP problems. It gives insight into the computational complexity in general and into the famous P vs NP questions.

Author(s): BYU Computer Science Department

NA Pages

Introduction to Theory of Computation Lecture Notes

These lecture notes give an introduction to the more fundamental parts of the theory of computation and begin by presenting finite automata: starting with deterministic and nondeterministic finite automata, their equivalence, and practical implications of these concepts. The lecture notes include sections on regular expressions and their relationship to finite automata, non-regular languages, and the Pumping Lemma to prove non-regularity. Myhill-Nerode Theorem: For understanding recognition of languages. The notes go further to present context-free languages, including their ambiguity and properties of closure. The pumping lemma for context-free languages is also discussed, while decidable and recognizable languages are informed by a deep underpinning in computational theory.

Author(s): Mahesh Viswanathan

NA Pages

Advanced Theory in Computation

This is an advanced set of notes on the analysis of algorithms and their complexity. Of interest in these notes are the topics on string matching algorithms, such as Knuth-Morris-Pratt and Boyer-Moore. Suffix trees and dictionary techniques are also part of the discussion here. Among the methods to be shown in a way of analyzing algorithm efficiency are amortized analysis and randomized algorithms. It also treats the pairing technique, Ziv-Lempel coding; further topics on statistical adversaries, portfolio selection, and reservation-price policies that are objects of other techniques discussed herein.

Author(s): Seoul National University

NA Pages