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.
Authored by Margaret Fleck and Sariel Har Peled, this
is a wide set of lecture notes on the theory of computation. These start with
the very basic objects such as strings and deterministic finite automata (DFAs)
before moving up to regular expressions and nondeterministic automata. This
course covers formal language theory, including some advanced topics such as
Turing machines, decidability, and several language-related problems. It is
intended that these notes afford a comprehensively broad yet deep exploration of
the formal languages, automata, and computability material with an excellent
bibliography that creates interest among students and researchers.
This
book surveys some of the most relevant theoretical concepts with computational
models. The limits of computation, undecidability of the Halting Problem,
several automata models, including both deterministic and nondeterministic
finite-state automata, pushdown automata, and Turing machines, are introduced.
The ending is dedicated to computational complexity, with NP-Completeness,
approximation algorithms, and hardness of approximation.
This book, written for graduates, covers
general subjects on computational models, logic circuits, and memory machines,
with advanced subjects being parallel computation, circuit complexity, and
space-time trade-offs; therefore, it's a very thorough course on computational
models and their complexities.
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.
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.
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.