Cybersecurity and Cyberforensics Conference最新文献

{"title":"On The Complexity of the Cayley Semigroup Membership Problem","authors":"Lukas Fleischer","doi":"10.4230/LIPIcs.CCC.2018.25","DOIUrl":"https://doi.org/10.4230/LIPIcs.CCC.2018.25","url":null,"abstract":"We investigate the complexity of deciding, given a multiplication table representing a semigroup S, a subset X of S and an element t of S, whether t can be expressed as a product of elements of X. It is well-known that this problem is NL-complete and that the more general Cayley groupoid membership problem, where the multiplication table is not required to be associative, is P-complete. For groups, the problem can be solved in deterministic log-space which raised the question of determining the exact complexity of this variant. Barrington, Kadau, Lange and McKenzie showed that for Abelian groups and for certain solvable groups, the problem is contained in the complexity class FOLL and they concluded that these variants are not hard for any complexity class containing PARITY. The more general case of arbitrary groups remained open. In this work, we show that for both groups and for commutative semigroups, the problem is solvable in qAC^0 (quasi-polynomial size circuits of constant depth with unbounded fan-in) and conclude that these variants are also not hard for any class containing PARITY. Moreover, we prove that NL-completeness already holds for the classes of 0-simple semigroups and nilpotent semigroups. Together with our results on groups and commutative semigroups, we prove the existence of a natural class of finite semigroups which generates a variety of finite semigroups with NL-complete Cayley semigroup membership, while the Cayley semigroup membership problem for the class itself is not NL-hard. We also discuss applications of our technique to FOLL.","PeriodicalId":246506,"journal":{"name":"Cybersecurity and Cyberforensics Conference","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126486309","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}

{"title":"On the Polynomial Parity Argument Complexity of the Combinatorial Nullstellensatz","authors":"Aleksandrs Belovs, G. Ivanyos, Youming Qiao, M. Santha, Siyi Yang","doi":"10.4230/LIPIcs.CCC.2017.30","DOIUrl":"https://doi.org/10.4230/LIPIcs.CCC.2017.30","url":null,"abstract":"The complexity class PPA consists of NP-search problems which are reducible to the parity principle in undirected graphs. It contains a wide variety of interesting problems from graph theory, combinatorics, algebra and number theory, but only a few of these are known to be complete in the class. Before this work, the known complete problems were all discretizations or combinatorial analogues of topological fixed point theorems. \u0000 \u0000Here we prove the PPA-completeness of two problems of radically different style. They are PPA-Circuit CNSS and PPA-Circuit Chevalley, related respectively to the Combinatorial Nullstellensatz and to the Chevalley-Warning Theorem over the two elements field GF(2). The input of these problems contain PPA-circuits which are arithmetic circuits with special symmetric properties that assure that the polynomials computed by them have always an even number of zeros. In the proof of the result we relate the multilinear degree of the polynomials to the parity of the maximal parse subcircuits that compute monomials with maximal multilinear degree, and we show that the maximal parse subcircuits of a PPA-circuit can be paired in polynomial time.","PeriodicalId":246506,"journal":{"name":"Cybersecurity and Cyberforensics Conference","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121732825","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}

{"title":"Two-player entangled games are NP-hard","authors":"Anand Natarajan, Thomas Vidick","doi":"10.4230/LIPIcs.CCC.2018.20","DOIUrl":"https://doi.org/10.4230/LIPIcs.CCC.2018.20","url":null,"abstract":"We show that the maximum success probability of players sharing quantum entanglement in a two-player game with classical questions of logarithmic length and classical answers of constant length is NP-hard to approximate to within constant factors. As a corollary, the inclusion $mathrm{NEXP}subseteqmathrm{MIP}^*$, first shown in [IV12] with three provers, holds with two provers only. The proof is based on a simpler, improved analysis of the low-degree test Raz and Safra (STOC'97) against two entangled provers.","PeriodicalId":246506,"journal":{"name":"Cybersecurity and Cyberforensics Conference","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117279193","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}

{"title":"Derandomizing Isolation in Space-Bounded Settings","authors":"D. Melkebeek, Gautam Prakriya","doi":"10.4230/LIPIcs.CCC.2017.5","DOIUrl":"https://doi.org/10.4230/LIPIcs.CCC.2017.5","url":null,"abstract":"We study the possibility of deterministic and randomness-efficient isolation in space-bounded models of computation: Can one efficiently reduce instances of computational problems to equivalent instances that have at most one solution? We present results for the NL-complete problem of reachability on digraphs, and for the LogCFL-complete problem of certifying acceptance on shallow semi-unbounded circuits. \u0000 \u0000A common approach employs small weight assignments that make the solution of minimum weight unique. The Isolation Lemma and other known procedures use Ω(n) random bits to generate weights of individual bitlength O(log n). We develop a derandomized version for both settings that uses O((log n)3/2) random bits and produces weights of bitlength O((log n)3/2) in logarithmic space. The construction allows us to show that every language in NL can be accepted by a nondeterministic machine that runs in polynomial time and O((log n)3/2) space, and has at most one accepting computation path on every input. Similarly, every language in LogCFL can be accepted by a nondeterministic machine equipped with a stack that does not count towards the space bound, that runs in polynomial time and O((log n)3/2) space, and has at most one accepting computation path on every input. \u0000 \u0000We also show that the existence of somewhat more restricted isolations for reachability on digraphs implies that NL can be decided in logspace with polynomial advice. A similar result holds for certifying acceptance on shallow semi-unbounded circuits and LogCFL.","PeriodicalId":246506,"journal":{"name":"Cybersecurity and Cyberforensics Conference","volume":"87 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116484914","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}

{"title":"Noise Stability Is Computable and Approximately Low-Dimensional","authors":"Anindya De, Elchanan Mossel, Joe Neeman","doi":"10.4230/LIPIcs.CCC.2017.10","DOIUrl":"https://doi.org/10.4230/LIPIcs.CCC.2017.10","url":null,"abstract":"Questions of noise stability play an important role in hardness of approximation in computer science as well as in the theory of voting. In many applications, the goal is to find an optimizer of noise stability among all possible partitions of R^n for n >= 1 to k parts with given Gaussian measures mu_1, ..., mu_k. We call a partition epsilon-optimal, if its noise stability is optimal up to an additive epsilon. In this paper, we give an explicit, computable function n(epsilon) such that an epsilon-optimal partition exists in R^{n(epsilon)}. This result has implications for the computability of certain problems in non-interactive simulation, which are addressed in a subsequent work.","PeriodicalId":246506,"journal":{"name":"Cybersecurity and Cyberforensics Conference","volume":"269 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127548536","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}

{"title":"The computational complexity of integer programming with alternations","authors":"Danny Nguyen, I. Pak","doi":"10.4230/LIPIcs.CCC.2017.6","DOIUrl":"https://doi.org/10.4230/LIPIcs.CCC.2017.6","url":null,"abstract":"We prove that integer programming with three quantifier alternations is $NP$-complete, even for a fixed number of variables. This complements earlier results by Lenstra and Kannan, which together say that integer programming with at most two quantifier alternations can be done in polynomial time for a fixed number of variables. As a byproduct of the proof, we show that for two polytopes $P,Q subset mathbb{R}^4$ , counting the projection of integer points in $Q backslash P$ is $#P$-complete. This contrasts the 2003 result by Barvinok and Woods, which allows counting in polynomial time the projection of integer points in $P$ and $Q$ separately.","PeriodicalId":246506,"journal":{"name":"Cybersecurity and Cyberforensics Conference","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132301923","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}

{"title":"Complexity-Theoretic Foundations of Quantum Supremacy Experiments","authors":"S. Aaronson, Lijie Chen","doi":"10.4230/LIPIcs.CCC.2017.22","DOIUrl":"https://doi.org/10.4230/LIPIcs.CCC.2017.22","url":null,"abstract":"In the near future, there will likely be special-purpose quantum computers with 40--50 high-quality qubits. This paper lays general theoretical foundations for how to use such devices to demonstrate \"quantum supremacy\": that is, a clear quantum speedup for some task, motivated by the goal of overturning the Extended Church-Turing Thesis as confidently as possible. \u0000 \u0000First, we study the hardness of sampling the output distribution of a random quantum circuit, along the lines of a recent proposal by the Quantum AI group at Google. We show that there's a natural average-case hardness assumption, which has nothing to do with sampling, yet implies that no polynomial-time classical algorithm can pass a statistical test that the quantum sampling procedure's outputs do pass. Compared to previous work -- for example, on BosonSampling and IQP -- the central advantage is that we can now talk directly about the observed outputs, rather than about the distribution being sampled. \u0000 \u0000Second, in an attempt to refute our hardness assumption, we give a new algorithm, inspired by Savitch's Theorem, for simulating a general quantum circuit with n qubits and depth d in polynomial space and dO(n) time. We then discuss why this and other known algorithms fail to refute our assumption. \u0000 \u0000Third, resolving an open problem of Aaronson and Arkhipov, we show that any strong quantum supremacy theorem -- of the form \"if approximate quantum sampling is classically easy, then the polynomial hierarchy collapses\"-- must be non-relativizing. This sharply contrasts with the situation for exact sampling. \u0000 \u0000Fourth, refuting a conjecture by Aaronson and Ambainis, we show that there is a sampling task, namely Fourier Sampling, with a 1 versus linear separation between its quantum and classical query complexities. \u0000 \u0000Fifth, in search of a \"happy medium\" between black-box and non-black-box arguments, we study quantum supremacy relative to oracles in P/poly. Previous work implies that, if one-way functions exist, then quantum supremacy is possible relative to such oracles. We show, conversely, that some computational assumption is needed: if SampBPP = SampBQP and NP ⊆ BPP, then quantum supremacy is impossible relative to oracles with small circuits.","PeriodicalId":246506,"journal":{"name":"Cybersecurity and Cyberforensics Conference","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131633123","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}

{"title":"A Note on Amortized Branching Program Complexity","authors":"Aaron Potechin","doi":"10.4230/LIPIcs.CCC.2017.4","DOIUrl":"https://doi.org/10.4230/LIPIcs.CCC.2017.4","url":null,"abstract":"In this paper, we show that while almost all functions require exponential size branching programs to compute, for all functions $f$ there is a branching program computing a doubly exponential number of copies of $f$ which has linear size per copy of $f$. This result disproves a conjecture about non-uniform catalytic computation, rules out a certain type of bottleneck argument for proving non-monotone space lower bounds, and can be thought of as a constructive analogue of Razborov's result that submodular complexity measures have maximum value $O(n)$.","PeriodicalId":246506,"journal":{"name":"Cybersecurity and Cyberforensics Conference","volume":"2014 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127432869","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}

{"title":"Separating Quantum Communication and Approximate Rank","authors":"Anurag Anshu, S. Ben-David, A. Garg, Rahul Jain, Robin Kothari, Troy Lee","doi":"10.4230/LIPIcs.CCC.2017.24","DOIUrl":"https://doi.org/10.4230/LIPIcs.CCC.2017.24","url":null,"abstract":"One of the best lower bound methods for the quantum communication complexity of a function H (with or without shared entanglement) is the logarithm of the approximate rank of the communication matrix of H. This measure is essentially equivalent to the approximate gamma_2 norm and generalized discrepancy, and subsumes several other lower bounds. All known lower bounds on quantum communication complexity in the general unbounded-round model can be shown via the logarithm of approximate rank, and it was an open problem to give any separation at all between quantum communication complexity and the logarithm of the approximate rank. \u0000In this work we provide the first such separation: We exhibit a total function H with quantum communication complexity almost quadratically larger than the logarithm of its approximate rank. We construct H using the communication lookup function framework of Anshu et al. (FOCS 2016) based on the cheat sheet framework of Aaronson et al. (STOC 2016). From a starting function F, this framework defines a new function H=F_G. Our main technical result is a lower bound on the quantum communication complexity of F_G in terms of the discrepancy of F, which we do via quantum information theoretic arguments. We show the upper bound on the approximate rank of F_G by relating it to the Boolean circuit size of the starting function F.","PeriodicalId":246506,"journal":{"name":"Cybersecurity and Cyberforensics Conference","volume":"132 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134242380","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}

{"title":"Conspiracies between Learning Algorithms, Circuit Lower Bounds and Pseudorandomness","authors":"I. Oliveira, R. Santhanam","doi":"10.4230/LIPIcs.CCC.2017.18","DOIUrl":"https://doi.org/10.4230/LIPIcs.CCC.2017.18","url":null,"abstract":"We prove several results giving new and stronger connections between learning, circuit lower bounds and pseudorandomness. Among other results, we show a generic learning speedup lemma, equivalences between various learning models in the exponential time and subexponential time regimes, a dichotomy between learning and pseudorandomness, consequences of non-trivial learning for circuit lower bounds, Karp-Lipton theorems for probabilistic exponential time, and NC$^1$-hardness for the Minimum Circuit Size Problem.","PeriodicalId":246506,"journal":{"name":"Cybersecurity and Cyberforensics Conference","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127107522","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}