Abstract Recursion and Intrinsic Complexity

Yiannis N. Moschovakis

doi:10.1017/9781108234238

This book presents and applies a framework for studying the complexity of algorithms. It is aimed at logicians, computer scientists, mathematicians and philosophers interested in the theory of computation and its foundations, and it is written at a level suitable for non-specialists. Part I provides an accessible introduction to abstract recursion theory and its connection with computability and complexity. This part is suitable for use as a textbook for an advanced undergraduate or graduate course: all the necessary elementary facts from logic, recursion theory, arithmetic and algebra are included. Part II develops and applies an extension of the homomorphism method due jointly to the author and Lou van den Dries for deriving lower complexity bounds for problems in number theory and algebra which (provably or plausibly) restrict all elementary algorithms from specified primitives. The book includes over 250 problems, from simple checks of the reader's understanding, to current open problems.

'… the author presents basic methods, approaches and results of the theory of abstract (ﬁrst-order) recursion and its relevance to the foundations of the theory of algorithms and computational complexity …'

Marat M. Arslanov Source: Mathematical Reviews Clippings

- Aa Reduce text
- Aa Enlarge text

View selected items
Save to my bookmarks
Export citations
Download PDF (zip)
Save to Kindle
Save to Dropbox
Save to Google Drive
Save content to
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to .

To save content items to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Please be advised that item(s) you selected are not available.
You are about to save
Your Kindle email address

Please provide your Kindle email.

@free.kindle.com @kindle.com (service fees apply)

By using this service, you agree that you will only keep content for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services

Metrics

Altmetric attention score

Total number of HTML views: 0

Total number of PDF views: 0 *

Loading metrics...

Total views: 0 *

Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.

Why this information is here

This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.

Accessibility Information

Accessibility compliance for the PDF of this book is currently unknown and may be updated in the future.

Abstract Recursion and Intrinsic Complexity

This Book has been cited by the following publications. This list is generated based on data provided by Crossref.

Book description

Reviews

Refine List

Actions for selected content:

Contents

Frontmatter
pp i-iv

Contents
pp v-viii

Introduction
pp 1-6

1 - Preliminaries
pp 7-46

Part I - Abstract (first order) recursion
pp 47-48

2 - Recursive (McCarthy) programs
pp 49-102

3 - Complexity theory for recursive programs
pp 103-126

Part II - Intrinsic complexity
pp 127-128

4 - The homomorphism method
pp 129-158

5 - Lower bounds from Presburger primitives
pp 159-170

6 - Lower bounds from division with remainder
pp 171-190

7 - Lower bounds from division and multiplication
pp 191-202

8 - Non-uniform complexity in N
pp 203-208

9 - Polynomial nullity (0-testing)
pp 209-228

References
pp 229-236

Symbol index
pp 237-238

General index
pp 239-243

Metrics

Altmetric attention score

Full text views

Book summary page views

Accessibility standard: Unknown

Why this information is here

Accessibility Information

Abstract Recursion and Intrinsic Complexity

Book description

Reviews

Refine List

Actions for selected content:

Save Search

Contents

Metrics

Altmetric attention score

Full text views

Book summary page views

Accessibility standard: Unknown

Why this information is here

Accessibility Information