惯性聚合 高效追踪和阅读你感兴趣的博客、新闻、科技资讯
阅读原文 在惯性聚合中打开

推荐订阅源

N
Netflix TechBlog - Medium
T
The Blog of Author Tim Ferriss
aimingoo的专栏
aimingoo的专栏
A
About on SuperTechFans
Stack Overflow Blog
Stack Overflow Blog
B
Blog RSS Feed
Microsoft Security Blog
Microsoft Security Blog
H
Hackread – Cybersecurity News, Data Breaches, AI and More
人人都是产品经理
人人都是产品经理
让小产品的独立变现更简单 - ezindie.com
让小产品的独立变现更简单 - ezindie.com
J
Java Code Geeks
Cyber Security Advisories - MS-ISAC
Cyber Security Advisories - MS-ISAC
B
Blog
MongoDB | Blog
MongoDB | Blog
L
LangChain Blog
WordPress大学
WordPress大学
小众软件
小众软件
IT之家
IT之家
腾讯CDC
月光博客
月光博客
量子位
Blog — PlanetScale
Blog — PlanetScale
P
Proofpoint News Feed
freeCodeCamp Programming Tutorials: Python, JavaScript, Git & More

cs.DS updates on arXiv.org

PAC Learning with Bandit Feedback: Sharp Sample Complexity in the Realizable Setting Algorithms with Polynomially-Improved Approximation Factors for the $2 \rightarrow q$ Norm, and Applications A computational phase transition for learning-to-sample from Ising models Covering vertices by sequential stars Fermi-Dirac machines as quantizations of neurons A Comprehensive Evaluation of Vertex Elimination Algorithms for Algorithmic Differentiation A Tight Bound on Localization of Electrical Flows Optimal Dimension-Free Sampling for Regularized Classification Reducing the Randomness in Partition Oracles for Bounded Degree Minor-Free Graphs Beyond the Half-Approximation: Fair and Efficient Online Class Matching Efficient Uniform Sampling of Surjections via their Profiles Tractable Maximization of Budgeted Phylogenetic Diversity on Networks Utilizing Node Scanwidth Fairness in Aggregation: Optimal Top-$k$ and Improved Full Ranking Learning-Augmented Online Scheduling with Parsimonious Preemption Entropy Equivalence Testing Lumberjack: Better Differentially Private Random Forests through Heavy Hitter Detection in Trees The Secretary Problem with a Stochastic Precursor Polynomial-Time Robust Multiclass Linear Classification under Gaussian Marginals Efficient Banzhaf-Based Data Valuation for $k$-Nearest Neighbors Classification Block-Sphere Vector Quantization An Approximation Algorithm for Graph Label Selection Iterative Chow Filtering for Learning with Distribution Shift Complexity of Non-Log-Concave Sampling in Fisher Information Stochastic Matching via Local Sparsification Finite Sample Bounds for Learning with Score Matching What is Learnable in Valiant's Theory of the Learnable? Provable Quantization with Randomized Hadamard Transform Min-Max Optimization Requires Exponentially Many Queries Fast and Compact Graph Cuts for the Boykov-Kolmogorov Algorithm A proximal gradient algorithm for composite log-concave sampling
PH = PSPACE
Valerii Sopin · 2014-11-04 · via cs.DS updates on arXiv.org

In this paper we show that PSPACE is equal to 4th level in the polynomial hierarchy. We also deduce a lot of important consequences. True quantified Boolean formula is a generalisation of the Boolean Satisfiability Problem, where determining of interpretation that satisfies a given Boolean formula is replaced by existence of Boolean functions that makes a given QBF to be tautology. Such functions are called the Skolem functions. The essential idea of the proof is to show that for any quantified Boolean formula $φ$ we can obtain a formula $φ'$ which is in the 4th level of the polynomial hierarchy, no more than polynomial in the size of a given $φ$, such that the truth of $φ$ can be determined from the truth of $φ'$. The idea is to skolemize, and then use additional formulas from the 2nd level of the polynomial hierarchy inside the skolemized prefix to enforce that the skolem variables indeed depend only on the universally quantified variables they are supposed to. However, some dependence is lost when the quantification is reversed. It is called "XOR issue" because the functional dependence can be expressed by means of an XOR formula. Thus, it is needed to locate these XORs, but there is no need to locate all chains with XORs: any chain includes a XOR of only two variables. The last can be done locally in each iteration (keep in mind the algebraic normal form (ANF)), when all arguments are specified, i.e. as a polynomial subroutine. Relativization is defeated due to the well-known fact: PH = PSPACE iff second-order logic over finite structures gains no additional power from the addition of a transitive closure operator. The exchange is possible due to finite possibilities for arguments. So, the theorems with oracles are not applicable since a random oracle is an arbitrary set. And that's why PH is infinite relative to a random oracle with probability 1.