Resource Bounded Measure and P Versus NP Problem-A Critical Study.

Date of Submission

December 2000

Date of Award

Winter 12-12-2001

Institute Name (Publisher)

Indian Statistical Institute

Document Type

Master's Dissertation

Degree Name

Master of Technology

Subject Name

Computer Science


Theoretical Statistics and Mathematics Unit (TSMU-Kolkata)


Sikdar, K. (TSMU-Kolkata; ISI)

Abstract (Summary of the Work)

This reports deals with the concept of resource-bounded measure that provides a quantative approach to deal with many questions of Structural Complexity Theory. Ia particular, we examine the consequences of the hypothesis that NP does not have p-measure 0 which is is a stronger hypothesis than that of NP ≠P.In the first chapter , we introduce the concept of resource-bounded measure and survey some basic results about it. We also give examples of classes with p-measure 0 or p-measure 1. In particular, (a) we give a sufficient condition for a class to have p-measure 0 in E and (b) we define , for each infinite language L € P, a class of languages XL that has p-measure 0. In the second chapter , we define a measure inside the class PSPACE. and survey some basic results about it. In the third chapter, we study nice properties like P-immunity and Incompressibility of languages in relation to resource bounded measure. Then we have made a small observation that if Bertman-Hartmanis conjecture is true then the class NPC has p-measure Oin E. Also we have shown that if Berman- Hartmanis conjecture holds and for any two language L1 and L2 € NPI we have L1ΔL2 € NPC then NP can have either measure 0 or it is non-measurable in E. In the fourth chapter , we present a notion of resource-bounded measure for P and other subexponential-time classes and examine its basic properties. In Chapter 5, we study the reasonableness and consequnces of the "hypethesis NP does not have p-measure 0".


ProQuest Collection ID:

Control Number


Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.


This document is currently not available here.