Perspectives in Computational Complexity

1. Front Matter

   Pages i-x

   PDF

2. Complexity Theory Basics: NP and NL

   • Vikraman Arvind

   Pages 1-22

3. Investigations Concerning the Structure of Complete Sets

   • Eric Allender

   Pages 23-35

4. Space Complexity of the Directed Reachability Problem over Surface-Embedded Graphs

   • N. Variyam Vinodchandran

   Pages 37-49

5. Algebraic Complexity Classes

   • Meena Mahajan

   Pages 51-75

6. A Selection of Lower Bounds for Arithmetic Circuits

   • Neeraj Kayal, Ramprasad Saptharishi

   Pages 77-115

7. Explicit Tensors

   • Markus Bläser

   Pages 117-130

8. Progress on Polynomial Identity Testing-II

   • Nitin Saxena

   Pages 131-146

9. Malod and the Pascaline

   • Bruno Poizat

   Pages 147-157

10. A Tutorial on Time and Space Bounds in Tree-Like Resolution

    • Jacobo Torán

    Pages 159-172

11. An Entropy-Based Proof for the Moore Bound for Irregular Graphs

    • S. Ajesh Babu, Jaikumar Radhakrishnan

    Pages 173-181

12. Permutation Groups and the Graph Isomorphism Problem

    • Sumanta Ghosh, Piyush P Kurur

    Pages 183-202

This book brings together contributions by leading researchers in computational complexity theory written in honor of Somenath Biswas on the occasion of his sixtieth birthday. They discuss current trends and exciting developments in this flourishing area of research and offer fresh perspectives on various aspects of complexity theory. The topics covered include arithmetic circuit complexity, lower bounds and polynomial identity testing, the isomorphism conjecture, space-bounded computation, graph isomorphism, resolution and proof complexity, entropy and randomness. Several chapters have a tutorial flavor. The aim is to make recent research in these topics accessible to graduate students and senior undergraduates in computer science and mathematics. It can also be useful as a resource for teaching advanced level courses in computational complexity.

• arithmetic circuits
• complete sets
• information theory
• lower bounds
• space and time complexity classes

• Department of Computer Science and Engineering, Indian Institute of Technology, Kanpur, India, Kanpur, India

  Manindra Agrawal

• CIT Campus, Institute of Mathematical Sciences, Chennai, India

  Vikraman Arvind

Manindra Agrawal is Professor at the Department of Computer Science and Engineering of the Indian Institute of Technology in Kanpur, India.

Vikraman Arvind is Professor at the Institute of Mathematical Sciences of the CIT Campus in Chennai, India.

Policies and ethics