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Fourier and Circulant Matrices are Not RigidFeb 19 2019The concept of matrix rigidity was first introduced by Valiant in [Val77]. Roughly speaking, a matrix is rigid if its rank cannot be reduced significantly by changing a small number of entries. There has been extensive interest in rigid matrices as Valiant ... More
Continuous Ordinary Differential Equations and Infinite Time Turing MachinesFeb 19 2019We consider Continuous Ordinary Differential Equations (CODE) y'=f(y), where f is a continuous function. They are known to always have solutions for a given initial condition y(0)=y0, these solutions being possibly non unique. We restrict to our attention ... More
Towards Optimal Depth Reductions for Syntactically Multilinear CircuitsFeb 19 2019We show that any $n$-variate polynomial computable by a syntactically multilinear circuit of size $\operatorname{poly}(n)$ can be computed by a depth-$4$ syntactically multilinear ($\Sigma\Pi\Sigma\Pi$) circuit of size at most $\exp\left({O\left(\sqrt{n\log ... More
Hardness of exact distance queries in sparse graphs through hub labelingFeb 19 2019A distance labeling scheme is an assignment of bit-labels to the vertices of an undirected, unweighted graph such that the distance between any pair of vertices can be decoded solely from their labels. An important class of distance labeling schemes is ... More
Error reduction of quantum algorithmsFeb 19 2019We give a technique to reduce the error probability of quantum algorithms that determine whether its input has a specified property of interest. The standard process of reducing this error is statistical processing of the results of multiple independent ... More
Approximations of Isomorphism and Logics with Linear-Algebraic OperatorsFeb 18 2019Invertible map equivalences are approximations of graph isomorphism that refine the well-known Weisfeiler-Leman method. They are parametrised by a number k and a set Q of primes. The intuition is that two graphs G and H which are equivalent with respect ... More
Complexity of the quorum intersection property of the Federated Byzantine Agreement SystemFeb 18 2019A Federated Byzantine Agreement System is defined as a pair $(V, Q)$ comprising a set of nodes $V$ and a quorum function $Q: V \mapsto 2^{2^{V}} \setminus \{\emptyset\}$ specifying for each node a set of subsets of nodes, called quorum slices. A subset ... More
Information-theoretic lower bounds for quantum sortingFeb 18 2019We analyze the quantum query complexity of sorting under partial information. In this problem, we are given a partially ordered set $P$ and are asked to identify a linear extension of $P$ using pairwise comparisons. For the standard sorting problem, in ... More
Beating Treewidth for Average-Case Subgraph IsomorphismFeb 18 2019For any fixed graph $G$, the subgraph isomorphism problem asks whether an $n$-vertex input graph has a subgraph isomorphic to $G$. A well-known algorithm of Alon, Yuster and Zwick (1995) efficiently reduces this to the "colored" version of the problem, ... More
Nearest neighbor decoding for Tardos fingerprinting codesFeb 17 2019Over the past decade, various improvements have been made to Tardos' collusion-resistant fingerprinting scheme [Tardos, STOC 2003], ultimately resulting in a good understanding of what is the minimum code length required to achieve collusion-resistance. ... More
Timeline-based planning: Expressiveness and ComplexityFeb 16 2019Timeline-based planning is an approach originally developed in the context of space mission planning and scheduling, where problem domains are modelled as systems made of a number of independent but interacting components, whose behaviour over time, the ... More
Parameterized Fine-Grained ReductionsFeb 14 2019During recent years the field of fine-grained complexity has bloomed to produce a plethora of results, with both applied and theoretical impact on the computer science community. The cornerstone of the framework is the notion of fine-grained reductions, ... More
Complexity-Theoretic Aspects of Expanding Cellular AutomataFeb 14 2019The expanding cellular automata (XCA) variant of cellular automata is investigated and characterized from a complexity-theoretical standpoint. The respective polynomial-time complexity class is shown to coincide with ${\le_{tt}^p}(\textbf{NP})$, that ... More
Which is the least complex explanation? Abduction and complexityFeb 14 2019It may happen that for a certain abductive problem there are several possible explanations, not all of them mutually compatible. What explanation is selected and which criteria are used to select it? This is the well-known problem of the selection of ... More
Reconstructing Trees from TracesFeb 13 2019We study the problem of learning a node-labeled tree given independent traces from an appropriately defined deletion channel. This problem, tree trace reconstruction, generalizes string trace reconstruction, which corresponds to the tree being a path. ... More
Counting Answers to Existential QuestionsFeb 13 2019Conjunctive queries select and are expected to return certain tuples from a relational database. We study the potentially easier problem of counting all selected tuples, rather than enumerating them. In particular, we are interested in the problem's parameterized ... More
New Results on Directed Edge Dominating SetFeb 13 2019We study a family of generalizations of Edge Dominating Set on directed graphs called Directed $(p,q)$-Edge Dominating Set. In this problem an arc $(u,v)$ is said to dominate itself, as well as all arcs which are at distance at most $q$ from $v$, or at ... More
Optimization problems with low SWaP tactical ComputingFeb 13 2019In a resource-constrained, contested environment, computing resources need to be aware of possible size, weight, and power (SWaP) restrictions. SWaP-aware computational efficiency depends upon optimization of computational resources and intelligent time ... More
On the achromatic number of signed graphsFeb 13 2019In this paper, we generalize the concept of complete coloring and achromatic number to 2-edge-colored graphs and signed graphs. We give some useful relationships between different possible definitions of such achromatic numbers and prove that computing ... More
Explicit lower bounds on strong simulation of quantum circuits in terms of $T$-gate countFeb 13 2019We investigate Clifford+$T$ quantum circuits with a small number of $T$-gates. Using the sparsification lemma, we identify time complexity lower bounds in terms of $T$-gate count below which a strong simulator would improve on the state-of-the-art $3$-SAT ... More
CSPs with Global Modular Constraints: Algorithms and Hardness via Polynomial RepresentationsFeb 13 2019We study the complexity of Boolean constraint satisfaction problems (CSPs) when the assignment must have Hamming weight in some congruence class modulo M, for various choices of the modulus M. Due to the known classification of tractable Boolean CSPs, ... More
Assessing Solution Quality of 3SAT on a Quantum Annealing PlatformFeb 13 2019When solving propositional logic satisfiability (specifically 3SAT) using quantum annealing, we analyze the effect the difficulty of different instances of the problem has on the quality of the answer returned by the quantum annealer. A high-quality response ... More
Computational Complexity and the Nature of Quantum MechanicsFeb 12 2019Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by having it follow from two main postulates ... More
Equivalent Polyadic Decompositions of Matrix Multiplication TensorsFeb 11 2019Invariance transformations of polyadic decompositions of matrix multiplication tensors define an equivalence relation on the set of such decompositions. In this paper, we present an algorithm to efficiently decide whether two polyadic decompositions of ... More
A Turing machine simulation by P systems without chargesFeb 11 2019It is well known that the kind of P systems involved in the definition of the P conjecture is able to solve problems in the complexity class $\mathbf{P}$ by leveraging the uniformity condition. Here we show that these systems are indeed able to simulate ... More
Solving QSAT in sublinear depthFeb 11 2019Among $\mathbf{PSPACE}$-complete problems, QSAT, or quantified SAT, is one of the most used to show that the class of problems solvable in polynomial time by families of a given variant of P systems includes the whole $\mathbf{PSPACE}$. However, most ... More
Solving QSAT in sublinear depthFeb 11 2019Feb 12 2019Among $\mathbf{PSPACE}$-complete problems, QSAT, or quantified SAT, is one of the most used to show that the class of problems solvable in polynomial time by families of a given variant of P systems includes the whole $\mathbf{PSPACE}$. However, most ... More
The word problem of the Brin-Thompson groups is coNP-completeFeb 11 2019We prove that the word problem of the Brin-Thompson group nV over a finite generating set is coNP-complete for every n \ge 2. It is known that the groups $n V$ are an infinite family of infinite, finitely presented, simple groups. We also prove that the ... More
A Simple Gap-producing Reduction for the Parameterized Set Cover ProblemFeb 11 2019Given an $n$-vertex bipartite graph $I=(S,U,E)$, the goal of set cover problem is to find a minimum sized subset of $S$ such that every vertex in $U$ is adjacent to some vertex of this subset. It is NP-hard to approximate set cover to within a $(1-o(1))\ln ... More
The Optimal Approximation Factor in Density EstimationFeb 10 2019Consider the following problem: given two arbitrary densities $q_1,q_2$ and a sample-access to an unknown target density $p$, find which of the $q_i$'s is closer to $p$ in total variation. A remarkable result due to Yatracos shows that this problem is ... More
Quantum distinguishing complexity, zero-error algorithms, and statistical zero knowledgeFeb 10 2019We define a new query measure we call quantum distinguishing complexity, denoted QD(f) for a Boolean function f. Unlike a quantum query algorithm, which must output a state close to |0> on a 0-input and a state close to |1> on a 1-input, a "quantum distinguishing ... More
On the Complexity of Exact Pattern Matching in Graphs: Determinism and Zig-Zag MatchingFeb 10 2019Exact pattern matching in labeled graphs is the problem of searching paths of a graph $G=(V,E)$ that spell the same string as the given pattern $P[1..m]$. This basic problem can be found at the heart of more complex operations on variation graphs in computational ... More
On modeling hard combinatorial optimization problems as linear programs: Refutations of the "unconditional impossibility" claimsFeb 10 2019There has been a series of developments in the recent literature (by essentially a same "circle" of authors) with the absolute/unconditioned (implicit or explicit) claim that there exists no abstraction of an NP-Complete combinatorial optimization problem ... More
Computational Complexity and the Nature of Quantum Mechanics (Extended version)Feb 09 2019Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by having it follow from two main postulates ... More
Detecting mixed-unitary quantum channels is NP-hardFeb 08 2019A 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 ... More
Generic reductions for in-place polynomial multiplicationFeb 08 2019The polynomial multiplication problem has attracted considerable attention since the early days of computer algebra, and several algorithms have been designed to achieve the best possible time complexity. More recently, efforts have been made to improve ... More
Fourier bounds and pseudorandom generators for product testsFeb 06 2019We study the Fourier spectrum of functions $f\colon \{0,1\}^{mk} \to \{-1,0,1\}$ which can be written as a product of $k$ Boolean functions $f_i$ on disjoint $m$-bit inputs. We prove that for every positive integer $d$, \[ \sum_{S \subseteq [mk]: |S|=d} ... More
$\mathsf{QMA}$ Lower Bounds for Approximate CountingFeb 06 2019We prove a query complexity lower bound for $\mathsf{QMA}$ protocols that solve approximate counting: estimating the size of a set given a membership oracle. This gives rise to an oracle $A$ such that $\mathsf{SBP}^A \not\subset \mathsf{QMA}^A$, resolving ... More
Noise in BosonSampling and the threshold of efficient classical simulabilityFeb 06 2019Feb 10 2019We study the quantum to classical transition in BosonSampling by analysing how $N$-boson interference is affected by inevitable noise in an experimental setup. We adopt the Gaussian noise model of Kalai and Kindler and relate it to realistic experimental ... More
Noise in BosonSampling and the threshold of efficient classical simulabilityFeb 06 2019Feb 07 2019We study the quantum to classical transition in BosonSampling by analysing how $N$-boson interference is affected by inevitable noise in an experimental setup. We adopt the Gaussian noise model of Kalai and Kindler and relate it to realistic experimental ... More
Non-cooperatively assembling large structures: a 2D pumping lemma cannot be as powerful as its 1D counterpartFeb 06 2019We show the first asymptotically efficient constructions in the so-called "noncooperative planar tile assembly" model. Algorithmic self-assembly is the study of the local, distributed, asynchronous algorithms ran by molecules to self-organise, in particular ... More
Firefighting on TreesFeb 06 2019In the Firefighter problem, introduced by Hartnell in 1995, a fire spreads through a graph while a player chooses which vertices to protect in order to contain it. In this paper, we focus on the case of trees and we consider as well the Fractional Firefighter ... More
Exact Optimization via Sums of Nonnegative Circuits and Sums of AM/GM ExponentialsFeb 06 2019We provide two hybrid numeric-symbolic optimization algorithms, computing exact sums of nonnegative circuits (SONC) and sums of arithmetic-geometric-exponentials (SAGE) decompositions. Moreover, we provide a hybrid numeric-symbolic decision algorithm ... More
On the Hardness and Inapproximability of Recognizing Wheeler GraphsFeb 05 2019In recent years several compressed indexes based on variants of the Borrows-Wheeler transformation have been introduced. Some of these index structures far more complex than a single string, as was originally done with the FM-index [Ferragina and Manzini, ... More
The Hardest HalfspaceFeb 05 2019We study the approximation of halfspaces $h:\{0,1\}^n\to\{0,1\}$ in the infinity norm by polynomials and rational functions of any given degree. Our main result is an explicit construction of the "hardest" halfspace, for which we prove polynomial and ... More
Expressive Power of Oblivious Consensus ProtocolsFeb 05 2019Population protocols are a formal model of computation by identical, anonymous mobile agents interacting in pairs. It has been shown that their computational power is rather limited: They can only compute the predicates expressible in Presburger arithmetic. ... More
Stochastic first-order methods: non-asymptotic and computer-aided analyses via potential functionsFeb 03 2019We 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 ... More
A Faster FPTAS for Knapsack Problem With Cardinality ConstraintFeb 03 2019Feb 13 2019We study the $K$-item knapsack problem (\ie, $1.5$-dimensional KP), which is a generalization of the famous 0-1 knapsack problem (\ie, $1$-dimensional KP) in which an upper bound $K$ is imposed on the number of items selected. This problem is of fundamental ... More
Knapsack Problem With Cardinality Constraint: A Faster FPTAS Through the Lens of Numerical Analysis and ApplicationsFeb 03 2019We study the $K$-item knapsack problem (\ie, $1.5$-dimensional knapsack problem), which is a generalization of the famous 0-1 knapsack problem (\ie, $1$-dimensional knapsack problem) in which an upper bound $K$ is imposed on the number of items selected. ... More
Grid Graph ReachabilityFeb 01 2019The reachability problem is to determine if there exists a path from one vertex to the other in a graph. Grid graphs are the class of graphs where vertices are present on the lattice points of a two-dimensional grid, and an edge can occur between a vertex ... More
Sharp Analysis for Nonconvex SGD Escaping from Saddle PointsFeb 01 2019In this paper, we prove that the simplest Stochastic Gradient Descent (SGD) algorithm is able to efficiently escape from saddle points and find an $(\epsilon, O(\epsilon^{0.5}))$-approximate second-order stationary point in $\tilde{O}(\epsilon^{-3.5})$ ... More
Counting of Teams in First-Order Team LogicsFeb 01 2019We study descriptive complexity of counting complexity classes in the range from $\#$P to $\#\cdot$NP. A corollary of Fagin's characterization of NP by existential second-order logic is that $\#$P can be logically described as the class of functions counting ... More
Finite semantics of polymorphism, complexity and the power of type fixpointsFeb 01 2019Many applications of denotational semantics, such as higher-order model checking or the complexity of normalization, rely on finite semantics for monomorphic type systems. We present two constructions of finite semantics for second-order Multiplicative-Additive ... More
Algorithmic counting of nonequivalent compact Huffman codesJan 31 2019It is known that the following five counting problems lead to the same integer sequence~$f_t(n)$: the number of nonequivalent compact Huffman codes of length~$n$ over an alphabet of $t$ letters, the number of `nonequivalent' canonical rooted $t$-ary trees ... More
Reachability in High Treewidth GraphsJan 31 2019Feb 05 2019Reachability is the problem of deciding whether there is a path from one vertex to the other in the graph. Standard graph traversal algorithms such as DFS and BFS take linear time to decide reachability however their space complexity is also linear. On ... More
The Semialgebraic Orbit ProblemJan 30 2019The Semialgebraic Orbit Problem is a fundamental reachability question that arises in the analysis of discrete-time linear dynamical systems such as automata, Markov chains, recurrence sequences, and linear while loops. An instance of the problem comprises ... More
A Pseudo-Deterministic RNC Algorithm for General Graph Perfect MatchingJan 29 2019Jan 31 2019We give an NC reduction from search to decision for the problem of finding a minimum weight perfect matching, provided edge weights are polynomially bounded. As a consequence, for settling the long-standing open problem of obtaining an NC perfect matching ... More
A Faster Solution to Smale's 17th Problem I: Real Binomial SystemsJan 28 2019Suppose $F:=(f_1,\ldots,f_n)$ is a system of random $n$-variate polynomials with $f_i$ having degree $\leq\!d_i$ and the coefficient of $x^{a_1}_1\cdots x^{a_n}_n$ in $f_i$ being an independent complex Gaussian of mean $0$ and variance $\frac{d_i!}{a_1!\cdots ... More
Parameterized Complexity of Safe SetJan 27 2019Jan 31 2019In this paper we study the problem of finding a small safe set $S$ in a graph $G$, i.e. a non-empty set of vertices such that no connected component of $G[S]$ is adjacent to a larger component in $G - S$. We enhance our understanding of the problem from ... More
Subspace arrangements, graph rigidity and derandomization through submodular optimizationJan 27 2019This paper presents a deterministic, strongly polynomial time algorithm for computing the matrix rank for a class of symbolic matrices (whose entries are polynomials over a field). This class was introduced, in a different language, by Lov\'asz [Lov] ... More
Bipartitioning of directed and mixed random graphsJan 27 2019We show that an intricate relation of cluster properties and optimal bipartitions, which takes place in undirected random graphs, extends to directed and mixed random graphs. In particular, the satisfability threshold coincides with the relative size ... More
The conjugate gradient algorithm on well-conditioned Wishart matrices is almost deteriministicJan 25 2019Feb 01 2019We prove that the number of iterations required to solve a random positive definite linear system with the conjugate gradient algorithm is almost deterministic for large matrices. We treat the case of Wishart matrices $W = XX^*$ where $X$ is $n \times ... More
Deterministic 2-Dimensional Temperature-1 Tile Assembly Systems Cannot ComputeJan 24 2019We consider non cooperative binding in so called `temperature 1', in deterministic (here called {\it confluent}) tile self-assembly systems (1-TAS) and prove the standing conjecture that such systems do not have universal computational power. We call ... More
Reachability Problem in Non-uniform Cellular AutomataJan 24 2019This paper deals with the CREP (Configuration REachability Problem) for non-uniform cellular automata (CAs). The cells of non-uniform CAs, we have considered here, can use different Wolfram's rules to generate their next states. We report an algorithm ... More
Deterministic constructions of high-dimensional sets with small dispersionJan 20 2019The dispersion of a point set $P\subset[0,1]^d$ is the volume of the largest box with sides parallel to the coordinate axes, which does not intersect $P$. Here, we show a construction of low-dispersion point sets, which can be deduced from solutions of ... More
Efficiently factoring polynomials modulo $p^4$Jan 20 2019Polynomial factoring has famous practical algorithms over fields-- finite, rational \& $p$-adic. However, modulo prime powers it gets hard as there is non-unique factorization and a combinatorial blowup ensues. For example, $x^2+p \bmod p^2$ is irreducible, ... More
Towards a General Direct Product Testing TheoremJan 18 2019The Direct Product encoding of a string $a\in \{0,1\}^n$ on an underlying domain $V\subseteq \binom{n}{k}$, is a function DP$_V(a)$ which gets as input a set $S\in V$ and outputs $a$ restricted to $S$. In the Direct Product Testing Problem, we are given ... More
Supportive Oracles for Parameterized Polynomial-Time Sub-Linear-Space Computations in Relation to L, NL, and PJan 17 2019We focus our attention onto polynomial-time sub-linear-space computation for decision problems, which are parameterized by size parameters $m(x)$, where the informal term "sub linear" means a function of the form $m(x)^{\varepsilon}\cdot polylog(|x|)$ ... More
Stoquastic PCP vs. RandomnessJan 16 2019The derandomization of MA, the probabilistic version of NP, is a long standing open question. In this work, we connect this problem to a variant of another major problem: the quantum PCP conjecture. Our connection goes through the surprising quantum characterization ... More
On the Complexity of Exact Pattern Matching in Graphs: Binary Strings and Bounded DegreeJan 16 2019Feb 08 2019Exact pattern matching in labeled graphs is the problem of searching paths of a graph $G=(V,E)$ that spell the same string as the pattern $P[1..m]$. This basic problem can be found at the heart of more complex operations on variation graphs in computational ... More
An Exponential Lower Bound on the Sub-Packetization of MSR CodesJan 16 2019An $(n,k,\ell)$-vector MDS code is a $\mathbb{F}$-linear subspace of $(\mathbb{F}^\ell)^n$ (for some field $\mathbb{F}$) of dimension $k\ell$, such that any $k$ (vector) symbols of the codeword suffice to determine the remaining $r=n-k$ (vector) symbols. ... More
On complexity of branching droplets in electrical fieldJan 15 2019Decanol droplets in a thin layer of sodium decanoate with sodium chloride exhibit bifurcation branching growth due to interplay between osmotic pressure, diffusion and surface tension. We aimed to evaluate if morphology of the branching droplets changes ... More
Existence of cube terms in finite finitely generated clonesJan 15 2019We study the problem of whether a given finite clone generated by finitely many operations contains a cube term and give both structural and algorithmic results. We show that if such a clone has a cube term then it has a cube term of dimension at most ... More
On geometric complexity theory: Multiplicity obstructions are stronger than occurrence obstructionsJan 14 2019Geometric Complexity Theory as initiated by Mulmuley and Sohoni in two papers (SIAM J Comput 2001, 2008) aims to separate algebraic complexity classes via representation theoretic multiplicities in coordinate rings of specific group varieties. The papers ... More
Lower bounds for multilinear bounded order ABPsJan 14 2019Proving super-polynomial size lower bounds for syntactic multilinear Algebraic Branching Programs(smABPs) computing an explicit polynomial is a challenging problem in Algebraic Complexity Theory. The order in which variables in $\{x_1,\ldots,x_n\}$ appear ... More
Topology is relevant (in the infinite-domain dichotomy conjecture for constraint satisfaction problems)Jan 14 2019The algebraic dichotomy conjecture for Constraint Satisfaction Problems (CSPs) of reducts of (infinite) finitely bounded homogeneous structures states that such CSPs are polynomial-time tractable when the model-complete core of the template has a pseudo-Siggers ... More
Model checking: the interval wayJan 12 2019Feb 11 2019[...] The most famous model checking (MC) techniques were developed from the late 80s, bearing in mind the well-known "point-based" temporal logics LTL and CTL. However, while the expressiveness of such logics is beyond doubt, there are some properties ... More
Model checking: the interval wayJan 12 2019Jan 15 2019[...] The most famous model checking (MC) techniques were developed from the late 80s, bearing in mind the well-known "point-based" temporal logics LTL and CTL. However, while the expressiveness of such logics is beyond doubt, there are some properties ... More
On Kernelization for Edge Dominating Set under Structural ParametersJan 11 2019In the NP-hard Edge Dominating Set problem (EDS) we are given a graph $G=(V,E)$ and an integer $k$, and need to determine whether there is a set $F\subseteq E$ of at most $k$ edges that are incident with all (other) edges of $G$. It is known that this ... More
On the Descriptive Complexity of Color CodingJan 10 2019Color coding is an algorithmic technique used in parameterized complexity theory to detect "small" structures inside graphs. The idea is to derandomize algorithms that first randomly color a graph and then search for an easily-detectable, small color ... More
Fragile Complexity of Comparison-Based AlgorithmsJan 09 2019We initiate a study of algorithms with a focus on the computational complexity of individual elements, and introduce the fragile complexity of comparison-based algorithms as the maximal number of comparisons any individual element takes part in. We give ... More
On NP-completeness of the cell formation problemJan 09 2019In the current paper we provide a proof of NP-completeness for the CFP problem with the fractional grouping efficacy objective. For this purpose we first consider the CFP with the linear objective minimizing the total number of exceptions and voids. Following ... More
Coercion-Resistant Voting in Linear Time via Fully Homomorphic Encryption: Towards a Quantum-Safe SchemeJan 08 2019Feb 05 2019We present an approach for performing the tallying work in the coercion-resistant JCJ voting protocol, introduced by Juels, Catalano, and Jakobsson, in linear time using fully homomorphic encryption (FHE). The suggested enhancement also paves the path ... More
Lower bounds for maximal matchings and maximal independent setsJan 08 2019Feb 08 2019There are distributed graph algorithms for finding maximal matchings and maximal independent sets in $O(\Delta + \log^* n)$ communication rounds; here $n$ is the number of nodes and $\Delta$ is the maximum degree. The lower bound by Linial (1987, 1992) ... More
On the Parameterized Complexity of $k$-Edge ColouringJan 07 2019Jan 08 2019For every fixed integer $k \geq 1$, we prove that $k$-Edge Colouring is fixed-parameter-tractable when parameterized by the number of vertices of maximum degree.
Near-Optimal Lower Bounds on the Threshold Degree and Sign-Rank of AC^0Jan 04 2019The threshold degree of a Boolean function $f\colon\{0,1\}^n\to\{0,1\}$ is the minimum degree of a real polynomial $p$ that represents $f$ in sign: $\mathrm{sgn}\; p(x)=(-1)^{f(x)}.$ A related notion is sign-rank, defined for a Boolean matrix $F=[F_{ij}]$ ... More
Clique-Width for Hereditary Graph ClassesJan 02 2019Jan 07 2019Clique-width is a well-studied graph parameter owing to its use in understanding algorithmic tractability: if the clique-width of a graph class ${\cal G}$ is bounded by a constant, a wide range of problems that are NP-complete in general can be shown ... More
Deciding the existence of minority termsJan 02 2019This paper investigates the computational complexity of deciding if a given finite idempotent algebra has a ternary term operation $m$ that satisfies the minority equations $m(y,x,x) \approx m(x,y,x) \approx m(x,x,y) \approx y$. We show that a common ... More
Almost Optimal Distribution-free Junta TestingJan 01 2019Jan 23 2019We consider the problem of testing whether an unknown $n$-variable Boolean function is a $k$-junta in the distribution-free property testing model, where the distance between function is measured with respect to an arbitrary and unknown probability distribution ... More
Algorithmically Efficient Syntactic Characterization of Possibility DomainsJan 01 2019We call domain any arbitrary subset of a Cartesian power of the set $\{0,1\}$ when we think of it as reflecting abstract rationality restrictions on vectors of two-valued judgments on a number of issues. In Computational Social Choice Theory, and in particular ... More
On the Approximability of Time Disjoint WalksDec 27 2018We introduce the combinatorial optimization problem Time Disjoint Walks. This problem takes as input a digraph $G$ with positive integer arc lengths, and $k$ pairs of vertices that each represent a trip demand from a source to a destination. The goal ... More
Approximate counting and NP search problemsDec 27 2018We study a new class of NP search problems, those which can be proved total in the theory $\mathrm{APC}_2$ of [Je\v{r}\'abek 2009]. This is an axiomatic theory in bounded arithmetic which can formalize standard combinatorial arguments based on approximate ... More
Quantum query complexity of symmetric oracle problemsDec 22 2018We study the query complexity of quantum learning problems in which the oracles form a group $G$ of unitary matrices. In the simplest case, one wishes to identify the oracle, and we find a description of the optimal success probability of a $t$-query ... More
Round elimination in exact communication complexityDec 21 2018We study two basic graph parameters, the chromatic number and the orthogonal rank, in the context of classical and quantum exact communication complexity. In particular, we consider two types of communication problems that we call promise equality and ... More
A Quantum Query Complexity Trichotomy for Regular LanguagesDec 11 2018Jan 23 2019We present a trichotomy theorem for the quantum query complexity of regular languages. Every regular language has quantum query complexity Theta(1), ~Theta(sqrt n), or Theta(n). The extreme uniformity of regular languages prevents them from taking any ... More
Binary Input Layer: Training of CNN models with binary input dataDec 09 2018For the efficient execution of deep convolutional neural networks (CNN) on edge devices, various approaches have been presented which reduce the bit width of the network parameters down to 1 bit. Binarization of the first layer was always excluded, as ... More
Kernelization of Packing ProblemsDec 07 2018Kernelization algorithms are polynomial-time reductions from a problem to itself that guarantee their output to have a size not exceeding some bound. For example, d-Set Matching for integers d>2 is the problem of finding a matching of size at least k ... More
Hard combinatorial problems and minor embeddings on lattice graphsDec 05 2018Today, hardware constraints are an important limitation on quantum adiabatic optimization algorithms. Firstly, computational problems must be formulated as quadratic unconstrained binary optimization (QUBO) in the presence of noisy coupling constants. ... More
An Inapproximability Result for the Target Set Selection Problem on Bipartite GraphsDec 04 2018Given an undirected graph $\mathcal{G}(V, E, \tau)$ modeling a 'social network', where each node $v$ is associated with a threshold value $\tau(v)$, a set of vertices $\mathcal{S} \subseteq V(\mathcal{G})$ (called 'seed nodes') is chosen initially. Now ... More
Small Hazard-free TransducersNov 29 2018Dec 15 2018Recently, an unconditional exponential separation between the hazard-free complexity and (standard) circuit complexity of explicit functions has been shown~\cite{ikenmeyer18complexity}. This raises the question: which classes of functions permit efficient ... More