Complexity Upper Bounds using Permutation Group theory

Declaration I declare that the thesis entitled Complexity Upper Bounds using Permutation Group theory submitted for the degree of Doctor of Philosophy is the record of the work carried out by me during January 2003 to January 2006 under the guidance of V. Arvind and has not formed the basis for the award of any degree, diploma, associateship, fellowship, titles in this University or any other University or other Institution of Higher learning. Certificate I certify that the thesis entitled Complexity Upper Bounds using Permutation Group theory submitted for the degree of Doctor of Philosophy by Piyush P Kurur is the record of research carried out by him during January 2003 to January 2006 under my guidance and supervision, and that this work has not formed the basis for the award of any degree, diploma, associ-ateship, fellowship or other titles in this University or any other University or Institution of higher learning. Acknowledgements During my stay at IMSc, I was fortunate to be in the company of some wonderful people who have directly or indirectly contributed to this thesis. Firstly I thank Arvind for supervising my work. It was he who introduced me to many of the fascinating topic in Computer Science. Working with him was a great experience in itself. In him I found a great teacher, a friend and a research collaborator. His contribution to this thesis is far more than what I could express in this limited space. I had the privilege to learn Computer Science and Mathematics through some excellent lectures at IMSc. I thank the group at IMSc, especially (especially Eric Allender and Lance Fortnow) and ANTS VI for their funds that helped me attend these conferences. I thank the National Board of Higher Mathematics (NBHM) and the Indian Association for Research in Computer Sciences (IARCS) for funding some of my research visits. Finally I would like to thank my friends for making the life in IMSc memorable and entertaining.