Electron. Colloquium Comput. Complex.最新文献

Dependency schemes in CDCL-based QBF solving: a proof-theoretic study 基于 CDCL 的 QBF 求解中的依赖方案：证明理论研究

Electron. Colloquium Comput. Complex. Pub Date : 2024-07-24 DOI: 10.4230/LIPIcs.FSTTCS.2023.38

Abhimanyu Choudhury, M. Mahajan

{"title":"Dependency schemes in CDCL-based QBF solving: a proof-theoretic study","authors":"Abhimanyu Choudhury, M. Mahajan","doi":"10.4230/LIPIcs.FSTTCS.2023.38","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSTTCS.2023.38","url":null,"abstract":"In Quantified Boolean Formulas QBFs, dependency schemes help to detect spurious or superfluous dependencies that are implied by the variable ordering in the quantifier prefix but are not essential for constructing countermodels. This detection can provably shorten refutations in specific proof systems, and is expected to speed up runs of QBF solvers. The proof system $$texttt{QCDCL}$$\u0000 QCDCL\u0000 recently defined by Beyersdorff and Boehm (LMCS 2023) abstracts the reasoning employed by QBF solvers based on conflict-driven clause-learning (CDCL) techniques. We show how to incorporate the use of dependency schemes into this proof system, either in a preprocessing phase, or in the propagations and clause learning, or both. We then show that when the reflexive resolution path dependency scheme $$texttt{D}^{texttt{rrs}}$$\u0000 \u0000 D\u0000 rrs\u0000 \u0000 is used, a mixed picture emerges: the proof systems that add $$texttt{D}^{texttt{rrs}}$$\u0000 \u0000 D\u0000 rrs\u0000 \u0000 to $$texttt{QCDCL}$$\u0000 QCDCL\u0000 in these three ways are not only incomparable with each other, but are also incomparable with the basic $$texttt{QCDCL}$$\u0000 QCDCL\u0000 proof system that does not use $$texttt{D}^{texttt{rrs}}$$\u0000 \u0000 D\u0000 rrs\u0000 \u0000 at all, as well as with several other resolution-based QBF proof systems. A notable fact is that all our separations are achieved through QBFs with bounded quantifier alternation.","PeriodicalId":11639,"journal":{"name":"Electron. Colloquium Comput. Complex.","volume":"69 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141808304","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

On blocky ranks of matrices 关于矩阵的块状等级

Electron. Colloquium Comput. Complex. Pub Date : 2024-03-06 DOI: 10.1007/s00037-024-00248-1

D. Avraham, A. Yehudayoff

引用次数: 3

Fractional Linear Matroid Matching is in quasi-NC 分数线性 Matroid 匹配处于准 NC 状态

Electron. Colloquium Comput. Complex. Pub Date : 2024-02-28 DOI: 10.48550/arXiv.2402.18276

Rohit Gurjar, Taihei Oki, Roshan Raj

引用次数: 0

Aaronson-Ambainis Conjecture Is True For Random Restrictions 阿伦森-安巴尼斯猜想对于随机限制是真的

Electron. Colloquium Comput. Complex. Pub Date : 2024-02-21 DOI: 10.48550/arXiv.2402.13952

Sreejata Kishor Bhattacharya

引用次数: 0

Optimal Pseudorandom Generators for Low-Degree Polynomials Over Moderately Large Fields 中等大字段上低度多项式的最佳伪随机发生器

Electron. Colloquium Comput. Complex. Pub Date : 2024-02-19 DOI: 10.48550/arXiv.2402.11915

Ashish Dwivedi, Zeyu Guo, Ben lee Volk

引用次数: 0

On Pigeonhole Principles and Ramsey in TFNP 论 TFNP 中的鸽洞原则和拉姆齐

Electron. Colloquium Comput. Complex. Pub Date : 2024-01-23 DOI: 10.48550/arXiv.2401.12604

Siddhartha Jain, Jiawei Li, Robert Robere, Zhiyang Xun

引用次数: 1

Unambiguous parity-query complexity 毫不含糊的奇偶校验查询复杂度

Electron. Colloquium Comput. Complex. Pub Date : 2024-01-20 DOI: 10.48550/arXiv.2401.11274

Dmytro Gavinsky

引用次数: 0

Upper Bounds on Communication in terms of Approximate Rank 基于近似秩的通信上界

Electron. Colloquium Comput. Complex. Pub Date : 2023-12-12 DOI: 10.1007/978-3-030-79416-3_7

A. Gál, Ridwan Syed

引用次数: 5

On Hardness Assumptions Needed for "Extreme High-End" PRGs and Fast Derandomization 关于“极高端”prg和快速非随机化所需的硬度假设

Electron. Colloquium Comput. Complex. Pub Date : 2023-11-20 DOI: 10.4230/LIPIcs.ITCS.2022.116

Ronen Shaltiel, Emanuele Viola

{"title":"On Hardness Assumptions Needed for \"Extreme High-End\" PRGs and Fast Derandomization","authors":"Ronen Shaltiel, Emanuele Viola","doi":"10.4230/LIPIcs.ITCS.2022.116","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITCS.2022.116","url":null,"abstract":"The hardness vs.~randomness paradigm aims to explicitly construct pseudorandom generators $G:{0,1}^r rightarrow {0,1}^m$ that fool circuits of size $m$, assuming the existence of explicit hard functions. A ``high-end PRG'' with seed length $r=O(log m)$ (implying BPP=P) was achieved in a seminal work of Impagliazzo and Wigderson (STOC 1997), assuming the high-end hardness assumption: there exist constants $0<beta<1<B$, and functions computable in time $2^{B cdot n}$ that cannot be computed by circuits of size $2^{beta cdot n}$. Recently, motivated by fast derandomization of randomized algorithms, Doron et al.~(FOCS 2020) and Chen and Tell (STOC 2021), construct ``extreme high-end PRGs'' with seed length $r=(1+o(1))cdot log m$, under qualitatively stronger assumptions. We study whether extreme high-end PRGs can be constructed from the following scaled version of the assumption which we call ``the extreme high-end hardness assumption'', and in which $beta=1-o(1)$ and $B=1+o(1)$. We give a partial negative answer, showing that certain approaches cannot yield a black-box proof. (A longer abstract with more details appears in the PDF file)","PeriodicalId":11639,"journal":{"name":"Electron. Colloquium Comput. Complex.","volume":"126 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73599176","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5

On correlation bounds against polynomials 关于多项式的相关界

Electron. Colloquium Comput. Complex. Pub Date : 2023-11-15 DOI: 10.4230/LIPIcs.CCC.2023.3

P. Ivanov, Liam Pavlovic, Emanuele Viola

{"title":"On correlation bounds against polynomials","authors":"P. Ivanov, Liam Pavlovic, Emanuele Viola","doi":"10.4230/LIPIcs.CCC.2023.3","DOIUrl":"https://doi.org/10.4230/LIPIcs.CCC.2023.3","url":null,"abstract":"We study the fundamental challenge of exhibiting explicit functions that have small correlation with low-degree polynomials over $mathbb{F}_{2}$. Our main contributions include: 1. In STOC 2020, CHHLZ introduced a new technique to prove correlation bounds. Using their technique they established new correlation bounds for low-degree polynomials. They conjectured that their technique generalizes to higher degree polynomials as well. We give a counterexample to their conjecture, in fact ruling out weaker parameters and showing what they prove is essentially the best possible. 2. We propose a new approach for proving correlation bounds with the central\"mod functions\", consisting of two steps: (I) the polynomials that maximize correlation are symmetric and (II) symmetric polynomials have small correlation. Contrary to related results in the literature, we conjecture that (I) is true. We argue this approach is not affected by existing\"barrier results\". 3. We prove our conjecture for quadratic polynomials. Specifically, we determine the maximum possible correlation between quadratic polynomials modulo 2 and the functions $(x_{1},dots,x_{n})to z^{sum x_{i}}$ for any $z$ on the complex unit circle; and show that it is achieved by symmetric polynomials. To obtain our results we develop a new proof technique: we express correlation in terms of directional derivatives and analyze it by slowly restricting the direction. 4. We make partial progress on the conjecture for cubic polynomials, in particular proving tight correlation bounds for cubic polynomials whose degree-3 part is symmetric.","PeriodicalId":11639,"journal":{"name":"Electron. Colloquium Comput. Complex.","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77508003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3