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  • No-Rainbow Problem is NP-Hard
    arXiv.cs.CC Pub Date : 2020-03-26
    Dmitriy Zhuk

    Surjective Constraint Satisfaction Problem (SCSP) is the problem of deciding whether there exists a surjective assignment to a set of variables subject to some specified constraints. In this paper we show that one of the most popular variants of the SCSP, called No-Rainbow Problem, is NP-Hard.

  • On the Complexity and Approximability of Optimal Sensor Selection and Attack for Kalman Filtering
    arXiv.cs.CC Pub Date : 2020-03-24
    Lintao Ye; Nathaniel Woodford; Sandip Roy; Shreyas Sundaram

    Given a linear dynamical system affected by stochastic noise, we consider the problem of selecting an optimal set of sensors (at design-time) to minimize the trace of the steady state a priori or a posteriori error covariance of the Kalman filter, subject to certain selection budget constraints. We show the fundamental result that there is no polynomial-time constant-factor approximation algorithm

  • A Topological Characterization of Modulo-p Arguments and Implications for Necklace Splitting
    arXiv.cs.CC Pub Date : 2020-03-26
    Aris Filos-Ratsikas; Alexandros Hollender; Katerina Sotiraki; Manolis Zampetakis

    The classes PPA-$p$ have attracted attention lately, because they are the main candidates for capturing the complexity of Necklace Splitting with $p$ thieves, for prime $p$. However, these classes are not known to have complete problems of a topological nature, which impedes any progress towards settling the complexity of the problem. On the contrary, such problems have been pivotal in obtaining completeness

  • Assignment and Pricing of Shared Rides in Ride-Sourcing using Combinatorial Double Auctions
    arXiv.cs.CC Pub Date : 2019-09-18
    Renos Karamanis; Eleftherios Anastasiadis; Panagiotis Angeloudis; Marc Stettler

    Transportation Network Companies employ dynamic pricing methods at periods of peak travel to incentivise driver participation and balance supply and demand for rides. Surge pricing multipliers are commonly used and are applied following demand and estimates of customer and driver trip valuations. Combinatorial double auctions have been identified as a suitable alternative, as they can achieve maximum

  • Bare quantum simultaneity versus classical interactivity in communication complexity
    arXiv.cs.CC Pub Date : 2019-11-04
    Dmitry Gavinsky

    A relational bipartite communication problem is presented that has an efficient quantum simultaneous-messages protocol, but no efficient classical two-way protocol.

  • Information-theoretically-sound non-interactive classical verification of quantum computing with trusted center
    arXiv.cs.CC Pub Date : 2020-03-24
    Tomoyuki Morimae

    The posthoc verification protocol [J. F. Fitzsimons, M. Hajdu{\v s}ek, and T. Morimae, Physical Review Letters {\bf120}, 040501 (2018)] enables an information-theoretically-sound non-interactive verification of quantum computing, but the message from the prover to the verifier is quantum and the verifier has to do single-qubit measurements. The Mahadev protocol removes these quantum parts, but the

  • Fair packing of independent sets
    arXiv.cs.CC Pub Date : 2020-03-25
    Nina Chiarelli; Matjaž Krnc; Martin Milanič; Ulrich Pferschy; Nevena Pivač; Joachim Schauer

    In this work we add a graph theoretical perspective to a classical problem of fairly allocating indivisible items to several agents. Agents have different profit valuations of items and we allow an incompatibility relation between pairs of items described in terms of a conflict graph. Hence, every feasible allocation of items to the agents corresponds to a partial coloring, that is, a collection of

  • Topology and adjunction in promise constraint satisfaction
    arXiv.cs.CC Pub Date : 2020-03-25
    Andrei Krokhin; Jakub Opršal; Marcin Wrochna; Stanislav Živný

    The approximate graph colouring problem concerns colouring a $k$-colourable graph with $c$ colours, where $c\geq k$. This problem naturally generalises to promise graph homomorphism and further to promise constraint satisfaction problems. Complexity analysis of all these problems is notoriously difficult. In this paper, we introduce two new techniques to analyse the complexity of promise CSPs: one

  • Message complexity of population protocols
    arXiv.cs.CC Pub Date : 2020-03-20
    Talley Amir; James Aspnes; David Doty; Mahsa Eftekhari H.; Eric Severson

    The standard population protocol model assumes that when two agents interact, each observes the entire state of the other agent. We initiate the study of the $\textbf{message complexity}$ for population protocols, where the state of an agent is divided into an externally-visible $\textbf{message}$ and an internal component, where only the message can be observed by the other agent in an interaction

  • $P\neq NP$
    arXiv.cs.CC Pub Date : 2020-03-22
    Tianrong Lin

    The whole discussions are divided into two parts, one is for $|\Sigma|\geq 2$ (general case), another is for $|\Sigma|=1$ (special case). The main contribution of the present paper is that a series of results are obtained. Specifically, we prove in general case that: (1) Let $L_1\in NP-P$ and $L_2\in P$, then the complexity of problem on reducibility from $L_1$ to $L_2$ is $\Omega(m^{p(|\omega|)})$

  • Lower Bounds on the Running Time of Two-Way Quantum Finite Automata and Sublogarithmic-Space Quantum Turing Machines
    arXiv.cs.CC Pub Date : 2020-03-22
    Zachary RemscrimMIT

    The two-way finite automaton with quantum and classical states (2QCFA), defined by Ambainis and Watrous, is a model of quantum computation whose quantum part is extremely limited; however, as they showed, 2QCFA are surprisingly powerful: a 2QCFA with only a single-qubit can recognize the language $L_{pal}=\{w \in \{a,b\}^*:w \text{ is a palindrome}\}$ with bounded error in expected time $2^{O(n)}$

  • The Power of a Single Qubit: Two-way Quantum Finite Automata and the Word Problem
    arXiv.cs.CC Pub Date : 2020-03-22
    Zachary RemscrimMIT

    The two-way finite automaton with quantum and classical states (2QCFA), defined by Ambainis and Watrous, is a model of quantum computation whose quantum part is extremely limited; however, as they showed, 2QCFA are surprisingly powerful: a 2QCFA, with a single qubit, can recognize, with bounded error, the language $L_{eq}=\{a^m b^m :m \in \mathbb{N}\}$ in expected polynomial time and the language $L_{pal}=\{w

  • 1 x 1 Rush Hour with Fixed Blocks is PSPACE-complete
    arXiv.cs.CC Pub Date : 2020-03-22
    Josh Brunner; Lily Chung; Erik D. Demaine; Dylan Hendrickson; Adam Hesterberg; Adam Suhl; Avi Zeff

    Consider $n^2-1$ unit-square blocks in an $n \times n$ square board, where each block is labeled as movable horizontally (only), movable vertically (only), or immovable -- a variation of Rush Hour with only $1 \times 1$ cars and fixed blocks. We prove that it is PSPACE-complete to decide whether a given block can reach the left edge of the board, by reduction from Nondeterministic Constraint Logic

  • The Computational Complexity of Evil Hangman
    arXiv.cs.CC Pub Date : 2020-03-22
    Jérémy Barbay; Bernardo Subercaseaux

    The game of Hangman is a classical asymmetric two player game in which one player, the setter, chooses a secret word from a language, that the other player, the guesser, tries to discover through single letter matching queries, answered by all occurrences of this letter if any. In the Evil Hangman variant, the setter can change the secret word during the game, as long as the new choice is consistent

  • Failure of Feasible Disjunction Property for $k$-DNF Resolution and NP-hardness of Automating It
    arXiv.cs.CC Pub Date : 2020-03-20
    Michal Garlík

    We show that for every integer $k \geq 2$, the Res($k$) propositional proof system does not have the weak feasible disjunction property. Next, we generalize a recent result of Atserias and M\"uller [FOCS, 2019] to Res($k$). We show that if NP is not included in P (resp. QP, SUBEXP) then for every integer $k \geq 1$, Res($k$) is not automatable in polynomial (resp. quasi-polynomial, subexponential)

  • Approximating the Existential Theory of the Reals
    arXiv.cs.CC Pub Date : 2018-10-02
    Argyrios Deligkas; John Fearnley; Themistoklis Melissourgos; Paul G. Spirakis

    The Existential Theory of the Reals (ETR) consists of existentially quantified Boolean formulas over equalities and inequalities of polynomial functions of variables in $\mathbb{R}$. In this paper we propose and study the approximate existential theory of the reals ($\epsilon$-ETR), in which the constraints only need to be satisfied approximately. We first show that when the domain of the variables

  • Sum of squares bounds for the ordering principle
    arXiv.cs.CC Pub Date : 2018-12-04
    Aaron Potechin

    In this paper, we analyze the sum of squares hierarchy (SOS) on the ordering principle on $n$ elements. We prove that degree $O(\sqrt{n}log(n))$ SOS can prove the ordering principle. We then show that this upper bound is essentially tight by proving that for any $\epsilon > 0$, SOS requires degree $\Omega(n^{\frac{1}{2} - \epsilon})$ to prove the ordering principle on $n$ elements.

  • Computing Maximum Matchings in Temporal Graphs
    arXiv.cs.CC Pub Date : 2019-05-13
    George B. Mertzios; Hendrik Molter; Rolf Niedermeier; Viktor Zamaraev; Philipp Zschoche

    Temporal graphs are graphs whose topology is subject to discrete changes over time. Given a static underlying graph $G$, a temporal graph is represented by assigning a set of integer time-labels to every edge $e$ of $G$, indicating the discrete time steps at which $e$ is active. We introduce and study the complexity of a natural temporal extension of the classical graph problem Maximum Matching, taking

  • Inexact Proximal-Point Penalty Methods for Constrained Non-Convex Optimization
    arXiv.cs.CC Pub Date : 2019-08-30
    Qihang Lin; Runchao Ma; Yangyang Xu

    In this paper, an inexact proximal-point penalty method is studied for constrained optimization problems, where the objective function is non-convex, and the constraint functions can also be non-convex. The proposed method approximately solves a sequence of subproblems, each of which is formed by adding to the original objective function a proximal term and quadratic penalty terms associated to the

  • Hardness of Bounded Distance Decoding on Lattices in $\ell_p$ Norms
    arXiv.cs.CC Pub Date : 2020-03-17
    Huck Bennett; Chris Peikert

    $ \newcommand{\Z}{\mathbb{Z}} \newcommand{\eps}{\varepsilon} \newcommand{\cc}[1]{\mathsf{#1}} \newcommand{\NP}{\cc{NP}} \newcommand{\problem}[1]{\mathrm{#1}} \newcommand{\BDD}{\problem{BDD}} $Bounded Distance Decoding $\BDD_{p,\alpha}$ is the problem of decoding a lattice when the target point is promised to be within an $\alpha$ factor of the minimum distance of the lattice, in the $\ell_{p}$ norm

  • A Generalization of Self-Improving Algorithms
    arXiv.cs.CC Pub Date : 2020-03-18
    Siu-Wing Cheng; Man-Kwun Chiu; Kai Jin; Man Ting Wong

    Ailon et al.~[SICOMP'11] proposed self-improving algorithms for sorting and Delaunay triangulation (DT) when the input instances $x_1,\cdots,x_n$ follow some unknown \emph{product distribution}. That is, $x_i$ comes from a fixed unknown distribution $\mathcal{D}_i$, and the $x_i$'s are drawn independently. After spending $O(n^{1+\varepsilon})$ time in a learning phase, the subsequent expected running

  • Tatamibari is NP-complete
    arXiv.cs.CC Pub Date : 2020-03-18
    Aviv Adler; Jeffrey Bosboom; Erik D. Demaine; Martin L. Demaine; Quanquan C. Liu; Jayson Lynch

    In the Nikoli pencil-and-paper game Tatamibari, a puzzle consists of an $m \times n$ grid of cells, where each cell possibly contains a clue among +, -, |. The goal is to partition the grid into disjoint rectangles, where every rectangle contains exactly one clue, rectangles containing + are square, rectangles containing - are strictly longer horizontally than vertically, rectangles containing | are

  • A Quadratic Lower Bound for Algebraic Branching Programs and Formulas
    arXiv.cs.CC Pub Date : 2019-11-26
    Prerona Chatterjee; Mrinal Kumar; Adrian She; Ben Lee Volk

    We show that any Algebraic Branching Program (ABP) computing the polynomial $\sum_{i = 1}^n x_i^n$ has at least $\Omega(n^2)$ vertices. This improves upon the lower bound of $\Omega(n\log n)$, which follows from the classical result of Baur and Strassen [Str73, BS83], and extends the results in [K19], which showed a quadratic lower bound for \emph{homogeneous} ABPs computing the same polynomial. Our

  • Sandwiches for Promise Constraint Satisfaction
    arXiv.cs.CC Pub Date : 2020-03-17
    Guofeng Deng; Ezzeddine El Sai; Trevor Manders; Peter Mayr; Poramate Nakkirt; Athena Sparks

    Promise Constraint Satisfaction Problems (PCSP) were proposed recently by Brakensiek and Guruswami arXiv:1704.01937 as a framework to study approximations for Constraint Satisfaction Problems (CSP). Informally a PCSP asks to distinguish between whether a given instance of a CSP has a solution or not even a specified relaxation can be satisfied. All currently known tractable PCSPs can be reduced in

  • Hard to Solve Instances of the Euclidean Traveling Salesman Problem
    arXiv.cs.CC Pub Date : 2018-08-08
    Stefan Hougardy; Xianghui Zhong

    The well known $4/3$ conjecture states that the integrality ratio of the subtour LP is at most $4/3$ for metric Traveling Salesman instances. We present a family of Euclidean Traveling Salesman instances for which we prove that the integrality ratio of the subtour LP converges to $4/3$. These instances (using the rounded Euclidean norm) turn out to be hard to solve exactly with Concorde, the fastest

  • Identifiability of Graphs with Small Color Classes by the Weisfeiler-Leman Algorithm
    arXiv.cs.CC Pub Date : 2019-07-05
    Frank Fuhlbrück; Johannes Köbler; Oleg Verbitsky

    As it is well known, the isomorphism problem for vertex-colored graphs with color multiplicity at most 3 is solvable by the classical 2-dimensional Weisfeiler-Leman algorithm (2-WL). On the other hand, the prominent Cai-F\"urer-Immerman construction shows that even the multidimensional version of the algorithm does not suffice for graphs with color multiplicity 4. We give an efficient decision procedure

  • Improved bounds for the sunflower lemma
    arXiv.cs.CC Pub Date : 2019-08-22
    Ryan Alweiss; Shachar Lovett; Kewen Wu; Jiapeng Zhang

    A sunflower with $r$ petals is a collection of $r$ sets so that the intersection of each pair is equal to the intersection of all. Erd\H{o}s and Rado proved the sunflower lemma: for any fixed $r$, any family of sets of size $w$, with at least about $w^w$ sets, must contain a sunflower. The famous sunflower conjecture is that the bound on the number of sets can be improved to $c^w$ for some constant

  • Sublinear-Time Language Recognition and Decision by One-Dimensional Cellular Automata
    arXiv.cs.CC Pub Date : 2019-09-12
    Augusto Modanese

    After an apparent hiatus of roughly 30 years, we revisit a seemingly neglected subject in the theory of (one-dimensional) cellular automata: sublinear-time computation. The model considered is that of ACAs, which are language acceptors whose acceptance condition depends on the states of all cells in the automaton. We prove a time hierarchy theorem for sublinear-time ACA classes, analyze their intersection

  • Four heads are better than three
    arXiv.cs.CC Pub Date : 2020-03-12
    Ville Salo

    We construct recursively-presented finitely-generated torsion groups which have bounded torsion and whose word problem is conjunctive equivalent (in particular positive and Turing equivalent) to a given recursively enumerable set. These groups can be interpreted as groups of finite state machines or as subgroups of topological full groups, on effective subshifts over other torsion groups. We define

  • Complexity of cutting planes and branch-and-bound in mixed-integer optimization
    arXiv.cs.CC Pub Date : 2020-03-10
    Amitabh Basu; Michele Conforti; Marco Di Summa; Hongyi Jiang

    We investigate the theoretical complexity of branch-and-bound (BB) and cutting plane (CP) algorithms for mixed-integer optimization. In particular, we study the relative efficiency of BB and CP, when both are based on the same family of disjunctions. We extend a result of Dash to the nonlinear setting which shows that for convex 0/1 problems, CP does at least as well as BB, with variable disjunctions

  • Magic: the Gathering is as Hard as Arithmetic
    arXiv.cs.CC Pub Date : 2020-03-11
    Stella Biderman

    Magic: the Gathering is a popular and famously complicated card game about magical combat. Recently, several authors including Chatterjee and Ibsen-Jensen (2016) and Churchill, Biderman, and Herrick (2019) have investigated the computational complexity of playing Magic optimally. In this paper we show that the ``mate-in-$n$'' problem for Magic is $\Delta^0_n$-hard and that optimal play in two-player

  • A generalized Sylvester-Gallai type theorem for quadratic polynomials
    arXiv.cs.CC Pub Date : 2020-03-11
    Shir Peleg; Amir Shpilka

    In this work we prove a version of the Sylvester-Gallai theorem for quadratic polynomials that takes us one step closer to obtaining a deterministic polynomial time algorithm for testing zeroness of $\Sigma^{[3]}\Pi\Sigma\Pi^{[2]}$ circuits. Specifically, we prove that if a finite set of irreducible quadratic polynomials $\mathcal{Q}$ satisfy that for every two polynomials $Q_1,Q_2\in \mathcal{Q}$

  • On Function Description
    arXiv.cs.CC Pub Date : 2020-02-19
    Rade Vuckovac

    The main result is that: function descriptions are not made equal, and they can be categorised in at least two categories using various computational methods for function evaluation. The result affects Kolmogorov complexity and Random Oracle Model notions. More precisely, the idea that the size of an object and the size of the smallest computer program defining that object is a ratio that represents

  • The Fine-Grained Complexity of Computing the Tutte Polynomial of a Linear Matroid
    arXiv.cs.CC Pub Date : 2020-03-07
    Andreas Björklund; Petteri Kaski

    We show that computing the Tutte polynomial of a linear matroid of dimension $k$ on $k^{O(1)}$ points over a field of $k^{O(1)}$ elements requires $k^{\Omega(k)}$ time unless the #ETH---a counting extension of the Exponential Time Hypothesis of Impagliazzo and Paturi [CCC 1999] due to Dell et al. [ACM TALG 2014]---is false. This holds also for linear matroids that admit a representation where every

  • Non-interactive classical verification of quantum computation
    arXiv.cs.CC Pub Date : 2019-11-19
    Gorjan Alagic; Andrew M. Childs; Alex B. Grilo; Shih-Han Hung

    In a recent breakthrough, Mahadev constructed an interactive protocol that enables a purely classical party to delegate any quantum computation to an untrusted quantum prover. In this work, we show that this same task can in fact be performed non-interactively and in zero-knowledge. Our protocols result from a sequence of significant improvements to the original four-message protocol of Mahadev. We

  • Multistage Graph Problems on a Global Budget
    arXiv.cs.CC Pub Date : 2019-12-09
    Klaus Heeger; Anne-Sophie Himmel; Frank Kammer; Rolf Niedermeier; Malte Renken; Andrej Sajenko

    Time-evolving or temporal graphs gain more and more popularity when studying the behavior of complex networks. In this context, the multistage view on computational problems is among the most natural frameworks. Roughly speaking, herein one studies the different (time) layers of a temporal graph (effectively meaning that the edge set may change over time, but the vertex set remains unchanged), and

  • Linear-Time Parameterized Algorithms with Limited Local Resources
    arXiv.cs.CC Pub Date : 2020-03-05
    Jianer Chen; Ying Guo; Qin Huang

    We propose a new (theoretical) computational model for the study of massive data processing with limited computational resources. Our model measures the complexity of reading the very large data sets in terms of the data size N and analyzes the computational cost in terms of a parameter k that characterizes the computational power provided by limited local computing resources. We develop new algorithmic

  • Simultaneous robust subspace recovery and semi-stability of quiver representations
    arXiv.cs.CC Pub Date : 2020-03-05
    Calin Chindris; Daniel Kline

    We consider the problem of simultaneously finding lower-dimensional subspace structures in a given $m$-tuple of possibly corrupted, high-dimensional data sets all of the same size. We refer to this problem as simultaneous robust subspace recovery (SRSR) and provide a quiver invariant theoretic approach to it. We show that SRSR is a particular case of the more general problem of effectively deciding

  • Barriers for rectangular matrix multiplication
    arXiv.cs.CC Pub Date : 2020-03-06
    Matthias Christandl; François Le Gall; Vladimir Lysikov; Jeroen Zuiddam

    We study the algorithmic problem of multiplying large matrices that are rectangular. We prove that the method that has been used to construct the fastest algorithms for rectangular matrix multiplication cannot give optimal algorithms. In fact, we prove a precise numerical barrier for this method. Our barrier improves the previously known barriers, both in the numerical sense, as well as in its generality

  • Towards a Complexity-theoretic Understanding of Restarts in SAT solvers
    arXiv.cs.CC Pub Date : 2020-03-04
    Chunxiao Li; Noah Fleming; Marc Vinyals; Toniann Pitassi; Vijay Ganesh

    Restarts are a widely used class of techniques integral to the efficiency of Conflict-Driven Clause Learning (CDCL) SAT solvers. While the utility of such policies has been well-established empirically, until now we didn't have a complexity-theoretic understanding of why restart policies are crucial to the power of CDCL SAT solvers. In this paper, we prove a series of theoretical results that characterize

  • Characterizations and approximability of hard counting classes below #P
    arXiv.cs.CC Pub Date : 2020-03-05
    Eleni Bakali; Aggeliki Chalki; Aris Pagourtzis

    An important objective of research in counting complexity is to understand which counting problems are approximable. In this quest, the complexity class TotP, a hard subclass of #P, is of key importance, as it contains self-reducible counting problems with easy decision version, thus eligible to be approximable. Indeed, most problems known so far to admit an fpras fall into this class. An open question

  • Maximum Clique in Disk-Like Intersection Graphs
    arXiv.cs.CC Pub Date : 2020-03-05
    Édouard Bonnet; Nicolas Grelier; Tillmann Miltzow

    We study the complexity of Maximum Clique in intersection graphs of convex objects in the plane. On the algorithmic side, we extend the polynomial-time algorithm for unit disks [Clark '90, Raghavan and Spinrad '03] to translates of any fixed convex set. We also generalize the efficient polynomial-time approximation scheme (EPTAS) and subexponential algorithm for disks [Bonnet et al. '18, Bonamy et

  • Detecting mixed-unitary quantum channels is NP-hard
    arXiv.cs.CC Pub Date : 2019-02-08
    Colin Do-Yan Lee; John Watrous

    A quantum channel is said to be a mixed-unitary channel if it can be expressed as a convex combination of unitary channels. We prove that, given the Choi representation of a quantum channel, it is NP-hard with respect to polynomial-time Turing reductions to determine whether or not that channel is a mixed-unitary channel. This hardness result holds even under the assumption that the channel is not

  • Direct Product Primality Testing of Graphs is GI-hard
    arXiv.cs.CC Pub Date : 2020-03-03
    Luca Calderoni; Luciano Margara; Moreno Marzolla

    We investigate the computational complexity of the graph primality testing problem with respect to the direct product (also known as Kronecker, cardinal or tensor product). In [1] Imrich proves that both primality testing and a unique prime factorization can be determined in polynomial time for (finite) connected and nonbipartite graphs. The author states as an open problem how results on the direct

  • A complexity chasm for solving sparse polynomial equations over $p$-adic fields
    arXiv.cs.CC Pub Date : 2020-02-29
    J. Maurice Rojas; Yuyu Zhu

    We reveal a complexity chasm, separating the trinomial and tetranomial cases, for solving univariate sparse polynomial equations over certain local fields. First, for any fixed field $K\in\{\mathbb{Q}_2,\mathbb{Q}_3,\mathbb{Q}_5,\ldots\}$, we prove that any polynomial $f\in\mathbb{Z}[x_1]$ with exactly $3$ monomial terms, degree $d$, and all coefficients having absolute value at most $H$, can be solved

  • Three-dimensional matching is NP-Hard
    arXiv.cs.CC Pub Date : 2020-02-29
    Shrinu Kushagra

    The standard proof of NP-Hardness of 3DM provides a power-$4$ reduction of 3SAT to 3DM. In this note, we provide a linear-time reduction. Under the exponential time hypothesis, this reduction improves the runtime lower bound from $2^{o(\sqrt[4]{m})}$ (under the standard reduction) to $2^{o(m)}$.

  • Descriptive complexity of real computation and probabilistic independence logic
    arXiv.cs.CC Pub Date : 2020-03-02
    Miika Hannula; Juha Kontinen; Jan Van den Bussche; Jonni Virtema

    We introduce a novel variant of BSS machines called Separate Branching BSS machines (S-BSS in short) and develop a Fagin-type logical characterisation for languages decidable in non-deterministic polynomial time by S-BSS machines. We show that NP on S-BSS machines is strictly included in NP on BSS machines and that every NP language on S-BSS machines is a countable union of closed sets in the usual

  • Hardness of Sparse Sets and Minimal Circuit Size Problem
    arXiv.cs.CC Pub Date : 2020-03-02
    Bin Fu

    We develop a polynomial method on finite fields to amplify the hardness of spare sets in nondeterministic time complexity classes on a randomized streaming model. One of our results shows that if there exists a $2^{n^{o(1)}}$-sparse set in $NTIME(2^{n^{o(1)}})$ that does not have any randomized streaming algorithm with $n^{o(1)}$ updating time, and $n^{o(1)}$ space, then $NEXP\not=BPP$, where a $f(n)$-sparse

  • Bi-Arc Digraphs and Conservative Polymorphisms
    arXiv.cs.CC Pub Date : 2016-08-11
    Pavol Hell; Akbar Rafiey; Arash Rafiey

    In this paper we study the class of bi-arc digraphs, important from two seemingly unrelated perspectives. On the one hand, they are precisely the digraphs that admit certain polymorphisms of interest in the study of constraint satisfaction problems; on the other hand, they are a very broad generalization of interval graphs. Bi-arc digraphs is the class of digraphs that admit conservative semilattice

  • Stochastic first-order methods: non-asymptotic and computer-aided analyses via potential functions
    arXiv.cs.CC Pub Date : 2019-02-03
    Adrien Taylor; Francis Bach

    We provide a novel computer-assisted technique for systematically analyzing first-order methods for optimization. In contrast with previous works, the approach is particularly suited for handling sublinear convergence rates and stochastic oracles. The technique relies on semidefinite programming and potential functions. It allows simultaneously obtaining worst-case guarantees on the behavior of those

  • Can Machine Learning Model with Static Features be Fooled: an Adversarial Machine Learning Approach
    arXiv.cs.CC Pub Date : 2019-04-20
    Rahim Taheri; Reza Javidan; Mohammad Shojafar; Vinod P; Mauro Conti

    The widespread adoption of smartphones dramatically increases the risk of attacks and the spread of mobile malware, especially on the Android platform. Machine learning-based solutions have been already used as a tool to supersede signature-based anti-malware systems. However, malware authors leverage features from malicious and legitimate samples to estimate statistical difference in-order to create

  • Subexponential-Time Algorithms for Sparse PCA
    arXiv.cs.CC Pub Date : 2019-07-26
    Yunzi Ding; Dmitriy Kunisky; Alexander S. Wein; Afonso S. Bandeira

    We study the computational cost of recovering a unit-norm sparse principal component $x \in \mathbb{R}^n$ planted in a random matrix, in either the Wigner or Wishart spiked model (observing either $W + \lambda xx^\top$ with $W$ drawn from the Gaussian orthogonal ensemble, or $N$ independent samples from $\mathcal{N}(0, I_n + \beta xx^\top)$, respectively). Prior work has shown that when the signal-to-noise

  • Tuning as convex optimisation: a polynomial tuner for multi-parametric combinatorial samplers
    arXiv.cs.CC Pub Date : 2020-02-26
    Maciej Bendkowski; Olivier Bodini; Sergey Dovgal

    Combinatorial samplers are algorithmic schemes devised for the approximate- and exact-size generation of large random combinatorial structures, such as context-free words, various tree-like data structures, maps, tilings, or even RNA sequences. In their multi-parametric variants, combinatorial samplers are adapted to combinatorial specifications with additional parameters, allowing for a more flexible

  • Two Player Hidden Pointer Chasing and Multi-Pass Lower Bounds in Turnstile Streams
    arXiv.cs.CC Pub Date : 2020-02-28
    Anay Mehrotra; Vibhor Porwal; Raghunath Tewari

    (Assadi, Chen, and Khanna, 2019) define a 4-player hidden-pointer-chasing ($\mathsf{HPC}^4$), and using it, give strong multi-pass lower bounds for graph problems in the streaming model of computation and a lower bound on the query complexity of sub-modular minimization. We present a two-player version ($\mathsf{HPC}^2$) of $\mathsf{HPC}^4$ that has matching communication complexity to $\mathsf{HPC}^4$

  • Estimating the entropy of shallow circuit outputs is hard
    arXiv.cs.CC Pub Date : 2020-02-27
    Alexandru Gheorghiu; Matty J. Hoban

    The decision problem version of estimating the Shannon entropy is the Entropy Difference problem (ED): given descriptions of two circuits, determine which circuit produces more entropy in its output when acting on a uniformly random input. The analogous problem with quantum circuits (QED) is to determine which circuit produces the state with greater von Neumann entropy, when acting on a fixed input

  • On Basing One-way Permutations on NP-hard Problems under Quantum Reductions
    arXiv.cs.CC Pub Date : 2018-04-27
    Nai-Hui Chia; Sean Hallgren; Fang Song

    A fundamental pursuit in complexity theory concerns reducing worst-case problems to average-case problems. There exist complexity classes such as PSPACE that admit worst-case to average-case reductions. However, for many other classes such as NP, the evidence so far is typically negative, in the sense that the existence of such reductions would cause collapses of the polynomial hierarchy(PH). Basing

  • Quantum Distributed Complexity of Set Disjointness on a Line
    arXiv.cs.CC Pub Date : 2020-02-26
    Frederic Magniez; Ashwin Nayak

    Given $x,y\in\{0,1\}^n$, Set Disjointness consists in deciding whether $x_i=y_i=1$ for some index $i \in [n]$. We study the problem of computing this function in a distributed computing scenario in which the inputs $x$ and $y$ are given to the processors at the two extremities of a path of length $d$. Set Disjointness on a Line was introduced by Le Gall and Magniez (PODC 2018) for proving lower bounds

  • Stochastic Matching with Few Queries: $(1-\varepsilon)$ Approximation
    arXiv.cs.CC Pub Date : 2020-02-27
    Soheil Behnezhad; Mahsa Derakhshan; MohammadTaghi Hajiaghayi

    Suppose that we are given an arbitrary graph $G=(V, E)$ and know that each edge in $E$ is going to be realized independently with some probability $p$. The goal in the stochastic matching problem is to pick a sparse subgraph $Q$ of $G$ such that the realized edges in $Q$, in expectation, include a matching that is approximately as large as the maximum matching among the realized edges of $G$. The maximum

  • Polynomial algorithms for p-dispersion problems in a 2d Pareto Front
    arXiv.cs.CC Pub Date : 2020-02-26
    Nicolas Dupin

    Having many best compromise solutions for bi-objective optimization problems, this paper studies p-dispersion problems to select $p\geqslant 2$ representative points in the Pareto Front(PF). Four standard variants of p-dispersion are considered. A novel variant, denoted Max-Sum-Neighbor p-dispersion, is introduced for the specific case of a 2d PF. Firstly, it is proven that $2$-dispersion and $3$-dispersion

  • Tree Polymatrix Games are PPAD-hard
    arXiv.cs.CC Pub Date : 2020-02-27
    Argyrios Deligkas; John Fearnley; Rahul Savani

    We prove that it is PPAD-hard to compute a Nash equilibrium in a tree polymatrix game with twenty actions per player. This is the first PPAD hardness result for a game with a constant number of actions per player where the interaction graph is acyclic. Along the way we show PPAD-hardness for finding an $\epsilon$-fixed point of a 2D LinearFIXP instance, when $\epsilon$ is any constant less than $(\sqrt{2}

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