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.
Preface.- 1. Complexity Theory Basics: NP and NL (Vikraman Arvind).- 2. Investigations Concerning the Structure of Complete Sets (Eric Allender).- 3. Space Complexity of the Directed Reachability Problem Over Surface-embedded Graphs (N.V. Vinodchandran).- 4. Algebraic Complexity Classes (Meena Mahajan).- 5. A Selection of Lower Bound Results for Arithmetic Circuits (Neeraj Kayal and Ramprasad Saptharishi).- 6. Explicit Tensors (Markus Bläser).- 7. Progress on Polynomial Identity Testing (Nitin Saxena).- 8. Malod and the Pascaline (Bruno Poizat).- 9. A Tutorial in Time and Space Bounds for Tree-like Resolution (Jacobo Torįn).- 10. An Entropy Based Proof for the Moore Bound for Irregular Graphs (S. Ajesh Babu and Jaikumar Radharishnan).- 11. Permutation Groups and the Graph Isomorphism Problem (Sumanta Ghosh and Piyush P. Kurur).
Preface.-
1. Complexity Theory Basics: NP and NL (Vikraman Arvind).-
2.
Investigations Concerning the Structure of Complete Sets (Eric Allender).-
3.
Space Complexity of the Directed Reachability Problem Over Surface-embedded
Graphs (N.V. Vinodchandran).-
4. Algebraic Complexity Classes (Meena
Mahajan).-
5. A Selection of Lower Bound Results for Arithmetic Circuits
(Neeraj Kayal and Ramprasad Saptharishi).-
6. Explicit Tensors (Markus
Bläser).-
7. Progress on Polynomial Identity Testing (Nitin Saxena).-
8.
Malod and the Pascaline (Bruno Poizat).-
9. A Tutorial in Time and Space
Bounds for Tree-like Resolution (Jacobo Torįn).-
10. An Entropy Based Proof
for the Moore Bound for Irregular Graphs (S. Ajesh Babu and Jaikumar
Radharishnan).-
11. Permutation Groups and the Graph Isomorphism Problem
(Sumanta Ghosh and Piyush P. Kurur).
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.
