Reducing the Number of Solutions of NP Functions

AbstractWe study whether one can prune solutions from NP functions. Though it is known that, unless surprising complexity class collapses occur, one cannot reduce the number of accepting paths of NP machines, we nonetheless show that it often is possible to reduce the number of solutions of NP functions. For finite cardinality types, we give a sufficient condition for such solution reduction. We also give absolute and conditional necessary conditions for solution reduction, and in particular we show that in many cases solution reduction is impossible unless the polynomial hierarchy collapses

Counting Classes Definedby Prime Numbers

ريف صفوف تعقيد جديدة لحاسبة تورينك اللاحتمية بزمن  P-NP-problem is the most important issue in computing theory and computational complexity,Through her study has been defined and studied the ranks of other complexity such ascoNP, PP, .. In this paper we have defined new complexity classes forpolynomial time nondeterministic Turing Machine using prime and composite numbersfor k-prime numbers  and we have proven that  is a subclass of it and the class is a subclass o

Reducing the Number of Solutions of NP Functions

We study whether one can prune solutions from NP functions. Though it is known that, unless surprising complexity class collapses occur, one cannot reduce the number of accepting paths of NP machines [Ogihara and Hemachandra 1993], we nonetheless show that it often is possible to reduce the number of solutions of NP functions. For finite cardinality types, we give a sufficient condition for such solution reduction. We also give absolute and conditional necessary conditions for solution reduction, and in particular we show that in many cases solution reduction is impossible unless the polynomial hierarchy collapses

The Consequences of Eliminating NP Solutions

Given a function based on the computation of an NP machine, can one in general eliminate some solutions? That is, can one in general decrease the ambiguity? This simple question remains, even after extensive study by many researchers over many years, mostly unanswered. However, complexity-theoretic consequences and enabling conditions are known. In this tutorial-style article we look at some of those, focusing on the most natural framings: reducing the number of solutions of NP functions, refining the solutions of NP functions, and subtracting from or otherwise shrinking #P functions. We will see how small advice strings are important here, but we also will see how increasing advice size to achieve robustness is central to the proof of a key ambiguity-reduction result for NP functions