Results 1  10
of
22,056
The P versus NP problem
 Clay Mathematical Institute; The Millennium Prize Problem
, 2000
"... The P versus NP problem is to determine whether every language accepted by some nondeterministic algorithm in polynomial time is also accepted by some (deterministic) algorithm in polynomial time. To define the problem precisely it is necessary to give a formal model of a computer. The standard comp ..."
Abstract

Cited by 18 (0 self)
 Add to MetaCart
The P versus NP problem is to determine whether every language accepted by some nondeterministic algorithm in polynomial time is also accepted by some (deterministic) algorithm in polynomial time. To define the problem precisely it is necessary to give a formal model of a computer. The standard
The P versus NP Problem in Quantum Physics
"... Song D., P versus NP problem in quantum physics ..."
The Status of the P versus NP Problem
"... When Moshe Vardi asked me to write this piece for CACM, my first reaction was the article could be written in two words Still open. ..."
Abstract

Cited by 25 (0 self)
 Add to MetaCart
When Moshe Vardi asked me to write this piece for CACM, my first reaction was the article could be written in two words Still open.
P versus NP problem solution
, 2004
"... Contains the solution of P versus NP compexity class relation problem. As expected, P � = NP. Idea of the proof is the following: Supposing P = NP we build a problem in class P of fixed timecomplexity degree, with the following trait: every problem from P reduces to it, thus leading to contradictio ..."
Abstract
 Add to MetaCart
Contains the solution of P versus NP compexity class relation problem. As expected, P � = NP. Idea of the proof is the following: Supposing P = NP we build a problem in class P of fixed timecomplexity degree, with the following trait: every problem from P reduces to it, thus leading
An Interesting Perspective to the P versus NP Problem
"... Abstract. We discuss the P versus NP problem from the perspective of addition operation about polynomial functions. Two contradictory propositions for the addition operation are presented. With the proposition that the sum of k (k ≤ n) polynomial functions on n always yields a polynomial function, ..."
Abstract
 Add to MetaCart
Abstract. We discuss the P versus NP problem from the perspective of addition operation about polynomial functions. Two contradictory propositions for the addition operation are presented. With the proposition that the sum of k (k ≤ n) polynomial functions on n always yields a polynomial function
Where the REALLY Hard Problems Are
 IN J. MYLOPOULOS AND R. REITER (EDS.), PROCEEDINGS OF 12TH INTERNATIONAL JOINT CONFERENCE ON AI (IJCAI91),VOLUME 1
, 1991
"... It is well known that for many NPcomplete problems, such as KSat, etc., typical cases are easy to solve; so that computationally hard cases must be rare (assuming P != NP). This paper shows that NPcomplete problems can be summarized by at least one "order parameter", and that the hard p ..."
Abstract

Cited by 683 (1 self)
 Add to MetaCart
It is well known that for many NPcomplete problems, such as KSat, etc., typical cases are easy to solve; so that computationally hard cases must be rare (assuming P != NP). This paper shows that NPcomplete problems can be summarized by at least one "order parameter", and that the hard
Proof verification and hardness of approximation problems
 IN PROC. 33RD ANN. IEEE SYMP. ON FOUND. OF COMP. SCI
, 1992
"... We show that every language in NP has a probablistic verifier that checks membership proofs for it using logarithmic number of random bits and by examining a constant number of bits in the proof. If a string is in the language, then there exists a proof such that the verifier accepts with probabilit ..."
Abstract

Cited by 797 (39 self)
 Add to MetaCart
in the proof (though this number is a very slowly growing function of the input length). As a consequence we prove that no MAX SNPhard problem has a polynomial time approximation scheme, unless NP=P. The class MAX SNP was defined by Papadimitriou and Yannakakis [82] and hard problems for this class include
Finitetime analysis of the multiarmed bandit problem
 Machine Learning
, 2002
"... Abstract. Reinforcement learning policies face the exploration versus exploitation dilemma, i.e. the search for a balance between exploring the environment to find profitable actions while taking the empirically best action as often as possible. A popular measure of a policy’s success in addressing ..."
Abstract

Cited by 817 (15 self)
 Add to MetaCart
Abstract. Reinforcement learning policies face the exploration versus exploitation dilemma, i.e. the search for a balance between exploring the environment to find profitable actions while taking the empirically best action as often as possible. A popular measure of a policy’s success in addressing
A Threshold of ln n for Approximating Set Cover
 JOURNAL OF THE ACM
, 1998
"... Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NPhar ..."
Abstract

Cited by 776 (5 self)
 Add to MetaCart
Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NP
Results 1  10
of
22,056