This note covers the following topics: Sets,
functions and other preliminaries, Formal Languages, Finite Automata ,
Regular Expressions, Turing Machines, Context-Free Languages, Rice's Theorem,
Time complexity, NP-Completeness, Space Complexity , Log Space, Oracle
machines and Turing Reducibility, Probabilistic Complexity, Approximation and
Optimisation, Complexity Hierarchy Theorems.
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.
Introduction
to the Theory of Computing is a course that undertakes
an intensive study of the underpinnings of the theory of computation. Beginning
with mathematical foundations, the course moves into regular operations and
expressions, and then into proofs on languages being nonregular and other
further treatments on regular languages. Other important topics include parse
trees, ambiguity, Chomsky normal form, pushdown automata, and Turing machines.
Further, the PDF discusses various types of Turing machines, the stack machine
model, and undecidable languages, making it a great starting point in the topic
of computability.
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.
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.
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.
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.