<p>In addition to the references already mentioned, you could check out </p>

<blockquote>
  <p>Xi Chen, Neeraj Kayal and Avi Wigderson (2011), <a href="http://dx.doi.org/10.1561/0400000043" rel="nofollow noreferrer">Partial Derivatives in Arithmetic Complexity and Beyond</a>, Foundations and Trends® in Theoretical Computer Science: Vol. 6: No. 1–2, pp 1-138. (<a href="http://www.math.ias.edu/~avi/PUBLICATIONS/ChenKaWi2011.pdf" rel="nofollow noreferrer">Freely available author's version</a>)</p>
</blockquote>

<p>Although the title makes it sound fairly specific, it's a pretty decent introduction. </p>

<p>I only know of one textbook devoted to this topic (Burgisser-Clausen-Shokrollahi "Algebraic Complexity Theory"), but it may not be the easiest introduction for beginners.</p>

CC BY-SA 4.0
2018-06-19T17:48:01.027Z
2018-06-19T17:48:01.027Z
Joshua Grochow
<p>This depends on what you want to do. For more structural questions there is a relatively recent survey by Meena Mahajan:</p>

<p>Meena Mahajan: Algebraic Complexity Classes. </p>

<p>There is also the book by Bürgisser:</p>

<p>Peter Bürgisser: Completeness and Reduction in Algebraic Complexity Theory.</p>

<p>For Geometric Complexity Theory, you might try the theses of <a href="http://www.cs.colorado.edu/~jgrochow/grochow-thesis.pdf" rel="noreferrer">Joshua Grochow</a> or <a href="http://digital.ub.uni-paderborn.de/ubpb/urn/urn:nbn:de:hbz:466:2-10472" rel="noreferrer">Christian Ikenmeyer</a>. I think both of them have introduction into the field, but I must admit that I have read neither of them.</p>

CC BY-SA 4.0
2018-06-19T12:33:44.833Z
Thanks but already checked these materials before,not the geometric one though.
ViX28
CC BY-SA 4.0
2018-06-19T12:27:57.193Z
2018-06-19T12:27:57.193Z
smengel
<p>Another good source that I am surprised hasn't been mentioned yet is the <a href="https://github.com/dasarpmar/lowerbounds-survey" rel="nofollow noreferrer">survey</a> by Ramprasad Saptharishi.</p>

CC BY-SA 4.0
2018-06-19T19:01:04.233Z
2018-06-19T19:01:04.233Z
Abhishek Shetty
<p><a href="https://nptel.ac.in/courses/106/104/106104221/" rel="nofollow noreferrer">This</a> is course on Arithmetic Circuit Complexity, offered by Prof Nitin Saxena (the S of AKS primality test). The syllabus and pre-requisites can be found <a href="https://onlinecourses.nptel.ac.in/noc20_cs47/preview" rel="nofollow noreferrer">here</a>.</p>

CC BY-SA 4.0
2020-09-01T08:38:25.500Z
2020-09-01T08:38:25.500Z
Gokul
<p>I am completely new to this field. I want to read the prelims and unfortunately, I don't see any book written for a beginner in this area. Can anyone give me some basic starting points/references(text/video) for a gentle introduction? I found these two given below.</p>
<p>Determinant versus permanent by Manindra Agarwal <a href="https://pdfs.semanticscholar.org/6a05/a4fe63e409ba040b890bbf5da0f3b1ca7085.pdf" rel="nofollow noreferrer">https://pdfs.semanticscholar.org/6a05/a4fe63e409ba040b890bbf5da0f3b1ca7085.pdf</a></p>
<p>Arithmetic circuits by Amir Shpilka</p>
<p><a href="https://www.cs.technion.ac.il/%7Eshpilka/publications/SY10.pdf" rel="nofollow noreferrer">https://www.cs.technion.ac.il/~shpilka/publications/SY10.pdf</a></p>
<p><em><strong>Is there any other material which can be more appropriate for a beginner?</strong></em></p>

CC BY-SA 4.0
2018-06-19T13:39:08.227Z
Vollmer's book has a section on arithmetic circuit complexity; that's fairly light.  Heribert Vollmer, "Introduction to Circuit Complexity".
Michaël Cadilhac
<cc.complexity-theory><circuit-complexity><arithmetic-circuits>
Reference request: Arithmetic circuit complexity
ViX28
# Reference request: Arithmetic circuit complexity

(Asked by: username_0 on 2018-06-19)

I am completely new to this field. I want to read the prelims and unfortunately, I don't see any book written for a beginner in this area. Can anyone give me some basic starting points/references(text/video) for a gentle introduction? I found these two given below.

Determinant versus permanent by Manindra Agarwal <https://pdfs.semanticscholar.org/6a05/a4fe63e409ba040b890bbf5da0f3b1ca7085.pdf>

Arithmetic circuits by Amir Shpilka

[https://www.cs.technion.ac.il/~shpilka/publications/SY10.pdf](https://www.cs.technion.ac.il/%7Eshpilka/publications/SY10.pdf)

***Is there any other material which can be more appropriate for a beginner?***

**Tags:** cc.complexity-theory, circuit-complexity, arithmetic-circuits
> **Comments:**
> **username_1**: Vollmer's book has a section on arithmetic circuit complexity; that's fairly light.  Heribert Vollmer, "Introduction to Circuit Complexity".  

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## 4 answers

### Answer by username_2 on 2018-06-19. Score: 4

In addition to the references already mentioned, you could check out

> Xi Chen, Neeraj Kayal and Avi Wigderson (2011), [Partial Derivatives in Arithmetic Complexity and Beyond](http://dx.doi.org/10.1561/0400000043), Foundations and Trends® in Theoretical Computer Science: Vol. 6: No. 1–2, pp 1-138. ([Freely available author's version](http://www.math.ias.edu/~avi/PUBLICATIONS/ChenKaWi2011.pdf))

Although the title makes it sound fairly specific, it's a pretty decent introduction.

I only know of one textbook devoted to this topic (Burgisser-Clausen-Shokrollahi "Algebraic Complexity Theory"), but it may not be the easiest introduction for beginners.


---

### Answer by username_3 on 2018-06-19. Score: 4

This depends on what you want to do. For more structural questions there is a relatively recent survey by Meena Mahajan:

Meena Mahajan: Algebraic Complexity Classes.

There is also the book by Bürgisser:

Peter Bürgisser: Completeness and Reduction in Algebraic Complexity Theory.

For Geometric Complexity Theory, you might try the theses of [Joshua Grochow](http://www.cs.colorado.edu/~jgrochow/grochow-thesis.pdf) or [Christian Ikenmeyer](http://digital.ub.uni-paderborn.de/ubpb/urn/urn:nbn:de:hbz:466:2-10472). I think both of them have introduction into the field, but I must admit that I have read neither of them.

> **Comments:**
> **username_0**: Thanks but already checked these materials before,not the geometric one though.  

---

### Answer by username_4 on 2018-06-19. Score: 3

Another good source that I am surprised hasn't been mentioned yet is the [survey](https://github.com/dasarpmar/lowerbounds-survey) by Ramprasad Saptharishi.


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### Answer by username_5 on 2020-09-01. Score: 3

[This](https://nptel.ac.in/courses/106/104/106104221/) is course on Arithmetic Circuit Complexity, offered by Prof Nitin Saxena (the S of AKS primality test). The syllabus and pre-requisites can be found [here](https://onlinecourses.nptel.ac.in/noc20_cs47/preview).


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