<p>There are some good books - 
 1. Computable Analysis - Pour-El and Richards (an older reference)
 2. Computable Analysis - Weihrauch </p>

<p>There's also the Blum-Shub-Smale Model, which is the model explored in "Complexity and Real Computation".</p>

<p>The complexity theory of computability of reals is explored in 
 1. Computational Complexity of real functions  - Ker-I Ko</p>

<p>A regular conference which explores this area is "Computability and Complexity in Analysis", held annually.</p>

CC BY-SA 3.0
2013-12-04T10:21:46.597Z
2013-12-04T10:21:46.597Z
Satyadev
<p>The website of <a href="http://cca-net.de/" rel="nofollow">Computability and Complexity in Analysis Network</a> has extensive <a href="http://cca-net.de/publications/bibliography.php" rel="nofollow">bibliography</a>. See their page for <a href="http://cca-net.de/publications/books.html" rel="nofollow">books</a>.</p>

<p>For computability, see </p>

<ul>
<li>Klaus Weihrauch, "<a href="http://www.fernuni-hagen.de/weihrauch/index_data/book.html" rel="nofollow">Computable Analysis</a>", 2010.</li>
</ul>

<p>It also has a chpater on complexity.</p>

<p>See also PhD theses of Jens Blanc and Andrej Bauer.</p>

<p>Another interesting paper is </p>

<ul>
<li>Viggo Stoltenberg-Hansen and John Tucker, "Computability on Topological
Spaces via Domain Representations", 1997.</li>
</ul>

CC BY-SA 3.0
2013-12-04T12:27:28.110Z
2013-12-04T12:27:28.110Z
Kaveh
<p>It would be extremely helpful if someone can suggest foundational textbooks on Recursive Analysis (Computability over Reals) which explains connections between Computability and the Topological properties of continuous sets. I could not find any, except "Recursive Analysis" by R.L. Goodstein but I dont have any feedback on that book. I would also like to ask for suggestions regarding a book on Complexity over Real Numbers which again deals with the connection between the complexity and the topology of a set. The only book I found on the net was "Complexity and Real Computation" by Lenore Blum et al but I am not sure if that is the book which I am looking for. Thanks in advance.</p>

<cc.complexity-theory><reference-request><soft-question><computability><computing-over-reals>
Foundational textbook(s) for Complexity and Computability on Real Numbers
swarnim_narayan
# Foundational textbook(s) for Complexity and Computability on Real Numbers

(Asked by: username_0 on 2013-12-04)

It would be extremely helpful if someone can suggest foundational textbooks on Recursive Analysis (Computability over Reals) which explains connections between Computability and the Topological properties of continuous sets. I could not find any, except "Recursive Analysis" by R.L. Goodstein but I dont have any feedback on that book. I would also like to ask for suggestions regarding a book on Complexity over Real Numbers which again deals with the connection between the complexity and the topology of a set. The only book I found on the net was "Complexity and Real Computation" by Lenore Blum et al but I am not sure if that is the book which I am looking for. Thanks in advance.

**Tags:** cc.complexity-theory, reference-request, soft-question, computability, computing-over-reals

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## 2 answers

### Answer by username_1 on 2013-12-04. Score: 2 | Accepted answer

There are some good books -
1. Computable Analysis - Pour-El and Richards (an older reference)
2. Computable Analysis - Weihrauch

There's also the Blum-Shub-Smale Model, which is the model explored in "Complexity and Real Computation".

The complexity theory of computability of reals is explored in
1. Computational Complexity of real functions - Ker-I Ko

A regular conference which explores this area is "Computability and Complexity in Analysis", held annually.


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### Answer by username_2 on 2013-12-04. Score: 1

The website of [Computability and Complexity in Analysis Network](http://cca-net.de/) has extensive [bibliography](http://cca-net.de/publications/bibliography.php). See their page for [books](http://cca-net.de/publications/books.html).

For computability, see

* Klaus Weihrauch, "[Computable Analysis](http://www.fernuni-hagen.de/weihrauch/index_data/book.html)", 2010.

It also has a chpater on complexity.

See also PhD theses of Jens Blanc and Andrej Bauer.

Another interesting paper is

* Viggo Stoltenberg-Hansen and John Tucker, "Computability on Topological
  Spaces via Domain Representations", 1997.


---

