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Quantum Lower Bounds for Approximate Counting via Laurent PolynomialsApr 18 2019This paper proves new limitations on the power of quantum computers to solve approximate counting -- that is, multiplicatively estimating the size of a nonempty set $S\subseteq [N]$. Given only a membership oracle for $S$, it is well known that approximate ... More
A doubly exponential upper bound on noisy EPR states for binary gamesApr 18 2019This paper initiates the study of a class of entangled-games, mono-state games, denoted by $(G,\psi)$, where $G$ is a two-player one-round game and $\psi$ is a bipartite state independent of the game $G$. In the mono-state game $(G,\psi)$, the players ... More
Samplers and extractors for unbounded functionsApr 17 2019Blasiok (SODA'18) recently introduced the notion of a subgaussian sampler, defined as an averaging sampler for approximating the mean of functions $f:\{0,1\}^m \to \mathbb{R}$ such that $f(U_m)$ has subgaussian tails, and asked for explicit constructions. ... More
The power word problemApr 17 2019In this work we introduce a new succinct variant of the word problem in a finitely generated group $G$, which we call the power word problem: the input word may contain powers $p^x$, where $p$ is a finite word over generators of $G$ and $x$ is a binary ... More
A Lower Bound for Relaxed Locally Decodable CodesApr 17 2019A locally decodable code (LDC) C:{0,1}^k -> {0,1}^n is an error correcting code wherein individual bits of the message can be recovered by only querying a few bits of a noisy codeword. LDCs found a myriad of applications both in theory and in practice, ... More
Approximating Cumulative Pebbling Cost is Unique Games HardApr 17 2019The cumulative pebbling complexity of a directed acyclic graph $G$ is defined as $\mathsf{cc}(G) = \min_P \sum_i |P_i|$, where the minimum is taken over all legal (parallel) black pebblings of $G$ and $|P_i|$ denotes the number of pebbles on the graph ... More
Extractors for small zero-fixing sourcesApr 16 2019A random variable $X$ is an $(n,k)$-zero-fixing source if for some subset $V\subseteq[n]$, $X$ is the uniform distribution on the strings $\{0,1\}^n$ that are zero on every coordinate outside of $V$. An $\epsilon$-extractor for $(n,k)$-zero-fixing sources ... More
Fast Commutative Matrix AlgorithmApr 16 2019We show that the product of an nx3 matrix and a 3x3 matrix over a commutative ring can be computed using 6n+3 multiplications. For two 3x3 matrices this gives us an algorithm using 21 multiplications. This is an improvement with respect to Makarov algorithm ... More
A Triangle Algorithm for Semidefinite Version of Convex Hull Membership ProblemApr 16 2019Given a subset $\mathbf{S}=\{A_1, \dots, A_m\}$ of $\mathbb{S}^n$, the set of $n \times n$ real symmetric matrices, we define its {\it spectrahull} as the set $SH(\mathbf{S}) = \{p(X) \equiv (Tr(A_1 X), \dots, Tr(A_m X))^T : X \in \mathbf{\Delta}_n\}$, ... More
From Hall's Marriage Theorem to Boolean Satisfiability and BackApr 15 2019Motivated by the application of Hall's Marriage Theorem in various LP-rounding problems, we introduce a generalization of the classical marriage problem (CMP) that we call the Fractional Marriage Problem. We show that the Fractional Marriage Problem is ... More
A Linear Upper Bound on the Weisfeiler-Leman Dimension of Graphs of Bounded GenusApr 15 2019The Weisfeiler-Leman (WL) dimension of a graph is a measure for the inherent descriptive complexity of the graph. While originally derived from a combinatorial graph isomorphism test called the Weisfeiler-Leman algorithm, the WL dimension can also be ... More
Sylvester-Gallai type theorems for quadratic polynomialsApr 12 2019We prove Sylvester-Gallai type theorems for quadratic polynomials. Specifically, we prove that if a finite collection $\mathcal Q$, of irreducible polynomials of degree at most $2$, satisfy that for every two polynomials $Q_1,Q_2\in {\mathcal Q}$ there ... More
Proceedings Joint International Workshop on Linearity & Trends in Linear Logic and ApplicationsApr 12 2019This volume contains a selection of papers presented at Linearity/TLLA 2018: Joint Linearity and TLLA workshops (part of FLOC 2018) held on July 7-8, 2018 in Oxford. Linearity has been a key feature in several lines of research in both theoretical and ... More
Parametrised Complexity of Model Checking and Satisfiability in Propositional Dependence LogicApr 12 2019In this paper, we initiate a systematic study of the parametrised complexity in the field of Dependence Logics which finds its origin in the Dependence Logic of V\"a\"an\"anen from 2007. We study a propositional variant of this logic (PDL) and investigate ... More
Complexity of full counting statistics of free quantum particles in entangled statesApr 12 2019We study the computational complexity of quantum-mechanical expectation values of single-particle operators in bosonic and fermionic multi-particle product states. Such expectation values appear, in particular, in full-counting-statistics problems. Depending ... More
Applications of the quantum algorithm for st-connectivityApr 12 2019We present quantum algorithms for various problems related to graph connectivity. We give simple and query-optimal algorithms for cycle detection and odd-length cycle detection (bipartiteness) using a reduction to st-connectivity. Furthermore, we show ... More
Quasi-popular Matchings, Optimality, and Extended FormulationsApr 11 2019Let $G = (A \cup B,E)$ be an instance of the stable marriage problem where every vertex ranks its neighbors in a strict order of preference. A matching $M$ in $G$ is popular if $M$ does not lose a head-to-head election against any matching $N$. That is, ... More
Quasi-popular Matchings, Optimality, and Extended FormulationsApr 11 2019Apr 17 2019Let G = ((A,B),E) be an instance of the stable marriage problem where every vertex ranks its neighbors in a strict order of preference. A matching M in G is popular if M does not lose a head-to-head election against any matching N. That is, \phi(M,N) ... More
NEEXP in MIP*Apr 11 2019We study multiprover interactive proof systems. The power of classical multiprover interactive proof systems, in which the provers do not share entanglement, was characterized in a famous work by Babai, Fortnow, and Lund (Computational Complexity 1991), ... More
Computational Intractability of Julia sets for real quadratic polynomialsApr 11 2019We show that there exist real parameters $c$ for which the Julia set $J_c$ of the quadratic map $z^2+c$ has arbitrarily high computational complexity. More precisely, we show that for any given complexity threshold $T(n)$, there exist a real parameter ... More
Real quadratic Julia sets can have arbitrarily high complexityApr 11 2019Apr 18 2019We show that there exist real parameters $c$ for which the Julia set $J_c$ of the quadratic map $z^2+c$ has arbitrarily high computational complexity. More precisely, we show that for any given complexity threshold $T(n)$, there exist a real parameter ... More
Locality of not-so-weak coloringApr 11 2019Many graph problems are locally checkable: a solution is globally feasible if it looks valid in all constant-radius neighborhoods. This idea is formalized in the concept of locally checkable labelings (LCLs), introduced by Naor and Stockmeyer (1995). ... More
P-Optimal Proof Systems for Each Set in NP but no Complete Disjoint NP-pairs Relative to an OracleApr 11 2019Apr 17 2019Consider the following conjectures: - $\mathsf{DisjNP}$: there exist no many-one complete disjoint NP-pairs. - $\mathsf{SAT}$: there exist no P-optimal proof systems for SAT. Pudl\'ak [Pud17] lists several conjectures (among these, $\mathsf{DisjNP}$ and ... More
The Circuit Complexity of InferenceApr 11 2019Belief propagation is one of the foundations of probabilistic and causal reasoning. In this paper, we study the circuit complexity of some of the various tasks it performs. Specifically, in the broadcast tree model (which has important applications to ... More
An FPT Algorithm for Max-Cut Parameterized by Crossing NumberApr 10 2019The Max-Cut problem is known to be NP-hard on general graphs, while it can be solved in polynomial time on planar graphs. In this paper, we present a fixed-parameter tractable algorithm for the problem on `almost' planar graphs: Given an $n$-vertex graph ... More
The Complexity of Subtree Intersection Representation of Chordal Graphs and Linear Time Chordal Graph GenerationApr 09 2019It is known that any chordal graph on $n$ vertices can be represented as the intersection of $n$ subtrees in a tree on $n$ nodes. This fact is recently used in [2] to generate random chordal graphs on $n$ vertices by generating $n$ subtrees of a tree ... More
Black-Box Complexity of the Binary Value FunctionApr 09 2019The binary value function, or BinVal, has appeared in several studies in theory of evolutionary computation as one of the extreme examples of linear pseudo-Boolean functions. Its unbiased black-box complexity was previously shown to be at most $\lceil ... More
Bridging between 0/1 and Linear Programming via Random WalksApr 09 2019Under the Strong Exponential Time Hypothesis, an integer linear program with $n$ Boolean-valued variables and $m$ equations cannot be solved in $c^n$ time for any constant $c < 2$. If the domain of the variables is relaxed to $[0,1]$, the associated linear ... More
The Complexity of Definability by Open First-Order FormulasApr 09 2019In this article we formally define and investigate the computational complexity of the Definability Problem for open first-order formulas (i.e., quantifier free first-order formulas) with equality. Given a logic $\mathbf{\mathcal{L}}$, the $\mathbf{\mathcal{L}}$-Definability ... More
More barriers for rank methods, via a "numeric to symbolic" transferApr 08 2019We prove new barrier results in arithmetic complexity theory, showing severe limitations of natural lifting (aka escalation) techniques. For example, we prove that even optimal rank lower bounds on $k$-tensors cannot yield non-trivial lower bounds on ... More
Junta correlation is testableApr 08 2019The problem of tolerant junta testing is a natural and challenging problem which asks if the property of a function having some specified correlation with a $k$-Junta is testable. In this paper we give an affirmative answer to this question: We show that ... More
Graph pattern detection: Hardness for all induced patterns and faster non-induced cyclesApr 07 2019We consider the pattern detection problem in graphs: given a constant size pattern graph $H$ and a host graph $G$, determine whether $G$ contains a subgraph isomorphic to $H$. Our main results are: * We prove that if a pattern $H$ contains a $k$-clique ... More
Linear-Time and Efficient Distributed Algorithms for List Coloring Graphs on SurfacesApr 07 2019In 1994, Thomassen proved that every planar graph is 5-list-colorable. In 1995, Thomassen proved that every planar graph of girth at least five is 3-list-colorable. His proofs naturally lead to quadratic-time algorithms to find such colorings. Here, we ... More
Semi-Countable Sets and their Application to Search ProblemsApr 07 2019We present the concept of the \emph{information efficiency of functions} as a technique to understand the interaction between information and computation. Based on these results we identify a new class of objects that we call \emph{Semi-Countable Sets}. ... More
The complexity of 3-colouring $H$-colourable graphsApr 05 2019We study the complexity of approximation on satisfiable instances for graph homomorphism problems. For a fixed graph $H$, the $H$-colouring problem is to decide whether a given graph has a homomorphism to $H$. By a result of Hell and Ne\v{s}et\v{r}il, ... More
Parameter estimation for integer-valued Gibbs distributionsApr 05 2019We consider the family of \emph{Gibbs distributions}, which are probability distributions over a discrete space $\Omega$ given by $\mu^\Omega_\beta(x)=\frac{e^{\beta H(x)}}{Z(\beta)}$. Here $H:\Omega\rightarrow \{0,1,\ldots,n\}$ is a fixed function (called ... More
Automating Resolution is NP-HardApr 05 2019We show that the problem of finding a Resolution refutation that is at most polynomially longer than a shortest one is NP-hard. In the parlance of proof complexity, Resolution is not automatizable unless P = NP. Indeed, we show it is NP-hard to distinguish ... More
The Complexity of the Ideal Membership Problem and Theta Bodies for Constrained Problems Over the Boolean DomainApr 05 2019Given an ideal $I$ and a polynomial $f$ the {Ideal Membership Problem} is to test if $f\in I$. This problem is a fundamental algorithmic problem with important applications and notoriously intractable. We study the complexity of the Ideal Membership Problem ... More
Quasi-polynomial Algorithms for List-coloring of Nearly Intersecting HypergraphsApr 04 2019A hypergraph $\mathcal{H}$ on $n$ vertices and $m$ edges is said to be {\it nearly-intersecting} if every edge of $\mathcal{H}$ intersects all but at most polylogarthmically many (in $m$ and $n$) other edges. Given lists of colors $\mathcal{L}(v)$, for ... More
Complexity of Counting Weighted Eulerian Orientations with ARSApr 04 2019Unique prime factorization of integers is taught in every high school. We define and explore a notion of unique prime factorization for constraint functions, and use this as a new tool to prove a complexity classification for counting weighted Eulerian ... More
Monte Carlo algorithms are very effective in finding the largest independent set in sparse random graphsApr 03 2019The effectiveness of stochastic algorithms based on Monte Carlo dynamics in solving hard optimization problems is mostly unknown. Beyond the basic statement that at a dynamical phase transition the ergodicity breaks and a Monte Carlo dynamics cannot sample ... More
Predicative proof theory of PDL and basic applicationsApr 03 2019Propositional dynamic logic (PDL) is presented in Sch\"{u}tte-style mode as one-sided semiformal tree-like sequent calculus Seq$_\omega^{\text{pdl}}$ with standard cut rule and the omega-rule with principal formulas $\left[ P^{\ast }\right] \!A$. The ... More
The Satisfiability Threshold for Non-Uniform Random 2-SATApr 03 2019Propositional satisfiability (SAT) is one of the most fundamental problems in computer science. Its worst-case hardness lies at the core of computational complexity theory, for example in the form of NP-hardness and the (Strong) Exponential Time Hypothesis. ... More
Solving tiling puzzles with quantum annealingApr 03 2019To solve tiling puzzles, such as "pentomino" or "tetromino" puzzles, we need to find the correct solutions out of numerous combinations of rotations or piece locations. Solving this kind of combinatorial optimization problem is a very difficult problem ... More
On the Complexity of Reachability in Parametric Markov Decision ProcessesApr 02 2019This paper studies parametric Markov decision processes (pMDPs), an extension to Markov decision processes (MDPs) where transitions probabilities are described by polynomials over a finite set of parameters. Fixing values for all parameters yields MDPs. ... More
The minimal probabilistic and quantum finite automata recognizing uncountably many languages with fixed cutpointsApr 02 2019It is known that 2-state binary and 3-state unary probabilistic finite automata and 2-state unary quantum finite automata recognize uncountably many languages with cutpoints. These results have been obtained by associating each recognized language with ... More
New relations and separations of conjectures about incompleteness in the fnite domainApr 02 2019Our main results are in the following three sections: 1. We prove new relations between proof complexity conjectures that are discussed in \cite{pu18}. 2. We investigate the existence of p-optimal proof systems for $\mathsf{TAUT}$, assuming the collapse ... More
New relations and separations of conjectures about incompleteness in the finite domainApr 02 2019Apr 05 2019Our main results are in the following three sections: 1. We prove new relations between proof complexity conjectures that are discussed in \cite{pu18}. 2. We investigate the existence of p-optimal proof systems for $\mathsf{TAUT}$, assuming the collapse ... More
An Algorithmic Theory of Integer ProgrammingApr 02 2019We study the general integer programming problem where the number of variables $n$ is a variable part of the input. We consider two natural parameters of the constraint matrix $A$: its numeric measure $a$ and its sparsity measure $d$. We show that integer ... More
Lower Bounds for Matrix FactorizationApr 02 2019We study the problem of constructing explicit families of matrices which cannot be expressed as a product of a few sparse matrices. In addition to being a natural mathematical question on its own, this problem appears in various incarnations in computer ... More
Simplified inpproximability of hypergraph coloring via t-agreeing familiesApr 02 2019We reprove the results on the hardness of approximating hypergraph coloring using a different technique based on bounds on the size of extremal $t$-agreeing families of $[q]^n$. Specifically, using theorems of Frankl-Tokushige [FT99], Ahlswede-Khachatrian ... More
Intersection multiplicity of a sparse curve and a low-degree curveApr 01 2019Let $F(x, y) \in \mathbb{C}[x,y]$ be a polynomial of degree $d$ and let $G(x,y) \in \mathbb{C}[x,y]$ be a polynomial with $t$ monomials. We want to estimate the maximal multiplicity of a solution of the system $F(x,y) = G(x,y) = 0$. Our main result is ... More
A Note on Hardness Frameworks and Computational Complexity of Xiangqi and JanggiMar 30 2019We review NP-hardness framework and PSPACE-hardness framework for a type of 2D platform games. We introduce a EXPTIME-hardness framework by defining some new gadgets. We use these hardness frameworks to analyse computational complexity of Xiangqi (Chinese ... More
Stabilizer Circuits, Quadratic Forms, and Computing Matrix RankMar 29 2019Apr 05 2019We show that a form of strong simulation for $n$-qubit quantum stabilizer circuits $C$ is computable in $O(s + n^\omega)$ time, where $\omega$ is the exponent of matrix multiplication. Solution counting for quadratic forms over $\mathbb{F}_2$ is also ... More
Stabilizer Circuits, Quadratic Forms, and Computing Matrix RankMar 29 2019We show that a form of strong simulation for $n$-qubit quantum stabilizer circuits $C$ is computable in $O(s + n^\omega)$ time, where $\omega$ is the exponent of matrix multiplication. Solution counting for quadratic forms over $\mathbb{F}_2$ is also ... More
DEEP-FRI: Sampling outside the box improves soundnessMar 28 2019Motivated by the quest for scalable and succinct zero knowledge arguments, we revisit worst-case-to-average-case reductions for linear spaces, raised by [Rothblum, Vadhan, Wigderson, STOC 2013]. We first show a sharp quantitative form of a theorem which ... More
Complete Disjoint coNP-Pairs but no Complete Total Polynomial Search Problems Relative to an OracleMar 28 2019Consider the following conjectures: H1: the set TFNP of all total polynomial search problems has no complete problems with respect to polynomial reductions. H2: there exists no many-one complete disjoint coNP-pair. We construct an oracle relative to which ... More
Complete Disjoint coNP-Pairs but no Complete Total Polynomial Search Problems Relative to an OracleMar 28 2019Apr 12 2019Consider the following conjectures: H1: the set TFNP of all total polynomial search problems has no complete problems with respect to polynomial reductions. H2: there exists no many-one complete disjoint coNP-pair. We construct an oracle relative to which ... More
Fourier Entropy-Influence Conjecture for Random Linear Threshold FunctionsMar 27 2019The Fourier-Entropy Influence (FEI) Conjecture states that for any Boolean function $f:\{+1,-1\}^n \to \{+1,-1\}$, the Fourier entropy of $f$ is at most its influence up to a universal constant factor. While the FEI conjecture has been proved for many ... More
Treewidth and Counting Projected Answer SetsMar 27 2019In this paper, we introduce novel algorithms to solve projected answer set counting (#PAs). #PAs asks to count the number of answer sets with respect to a given set of projected atoms, where multiple answer sets that are identical when restricted to the ... More
Complexity Thresholds in Inclusion LogicMar 26 2019Logics with team semantics provide alternative means for logical characterization of complexity classes. Both dependence and independence logic are known to capture non-deterministic polynomial time, and the frontiers of tractability in these logics are ... More
Faster Random $k$-CNF SatisfiabilityMar 25 2019We describe an algorithm to solve the problem of Boolean CNF-Satisfiability when the input formula is chosen randomly. We build upon the algorithms of Sch{\"{o}}ning 1999 and Dantsin et al.~in 2002. The Sch{\"{o}}ning algorithm works by trying many possible ... More
Trainable Time Warping: Aligning Time-Series in the Continuous-Time DomainMar 21 2019DTW calculates the similarity or alignment between two signals, subject to temporal warping. However, its computational complexity grows exponentially with the number of time-series. Although there have been algorithms developed that are linear in the ... More
Almost Tight Lower Bounds for Hard Cutting Problems in Embedded GraphsMar 20 2019We prove essentially tight lower bounds, conditionally to the Exponential Time Hypothesis, for two fundamental but seemingly very different cutting problems on surface-embedded graphs: the Shortest Cut Graph problem and the Multiway Cut problem. A cut ... More
The Average-Case Complexity of Counting Cliques in Erdős-Rényi HypergraphsMar 19 2019The complexity of clique problems on Erdos-Renyi random graphs has become a central topic in average-case complexity. Algorithmic phase transitions in these problems have been shown to have broad connections ranging from mixing of Markov chains to information-computation ... More
Semantic programming: method $Δ_0^p$-enrichments and polynomial computable fixed pointsMar 19 2019Computer programs fast entered in our live and the questions associated with the execution of these programs have become the most relevant in our days. Programs should work efficiently, i.e. work as quickly as possible and spend as little resources as ... More
How Hard Is Robust Mean Estimation?Mar 19 2019Robust mean estimation is the problem of estimating the mean $\mu \in \mathbb{R}^d$ of a $d$-dimensional distribution $D$ from a list of independent samples, an $\epsilon$-fraction of which have been arbitrarily corrupted by a malicious adversary. Recent ... More
One-Way Topological Automata and the Tantalizing Effects of Their Topological FeaturesMar 18 2019We cast new light on the existing models of 1-way deterministic topological automata by introducing a new, convenient model, in which, as each input symbol is read, an interior system of an automaton, known as a configuration, continues to evolve in a ... More
Token Swapping on TreesMar 16 2019The input to the token swapping problem is a graph with vertices $v_1, v_2, \ldots, v_n$, and $n$ tokens with labels $1, 2, \ldots, n$, one on each vertex. The goal is to get token $i$ to vertex $v_i$ for all $i= 1, \ldots, n$ using a minimum number of ... More
Proportionally dense subgraph of maximum size: complexity and approximationMar 15 2019Apr 10 2019We define a proportionally dense subgraph (PDS) as an induced subgraph of a graph with the property that each vertex in the PDS is adjacent to proportionally as many vertices in the subgraph as in the graph. We prove that the problem of finding a PDS ... More
Deterministic Approximation of Random Walks in Small SpaceMar 15 2019We give a deterministic, nearly logarithmic-space algorithm that given an undirected graph $G$, a positive integer $r$, and a set $S$ of vertices, approximates the conductance of $S$ in the $r$-step random walk on $G$ to within a factor of $1+\epsilon$, ... More
LIKE Patterns and ComplexityMar 14 2019We investigate the expressive power and complexity questions for the LIKE operator in SQL.
Maximum Cut Parameterized by Crossing NumberMar 14 2019Given an edge-weighted graph G on n nodes, the NP-hard Max-Cut problem asks for a node bipartition such that the sum of edge weights joining the different partitions is maximized. We propose a fixed-parameter tractable algorithm parameterized by the number ... More
New Dependencies of Hierarchies in Polynomial OptimizationMar 12 2019We compare four key hierarchies for solving Constrained Polynomial Optimization Problems (CPOP): Sum of Squares (SOS), Sum of Diagonally Dominant Polynomials (SDSOS), Sum of Nonnegative Circuits (SONC), and the Sherali Adams (SA) hierarchies. We prove ... More
Counting Polygon Triangulations is HardMar 12 2019We prove that it is $\#\mathsf{P}$-complete to count the triangulations of a (non-simple) polygon.
The relationship between word complexity and computational complexity in subshiftsMar 11 2019We prove several results about the relationship between the word complexity function of a subshift and the set of Turing degrees of points of the subshift, which we call the Turing spectrum. Among other results, we show that a Turing spectrum can be realized ... More
Knowledge compilation languages as proof systemsMar 10 2019In this paper, we study proof systems in the sense of Cook-Reckhow for problems that are higher in the polynomial hierarchy than coNP, in particular, #SAT and maxSAT. We start by explaining how the notion of Cook-Reckhow proof systems can be apply to ... More
How fast can we reach a target vertex in stochastic temporal graphs?Mar 08 2019Temporal graphs are used to abstractly model real-life networks that are inherently dynamic in nature. Given a static underlying graph $G=(V,E)$, a temporal graph on $G$ is a sequence of snapshots $G_t$, one for each time step $t\geq 1$. In this paper ... More
Computing Exact Solutions of Consensus Halving and the Borsuk-Ulam TheoremMar 07 2019We study the problem of finding an exact solution to the consensus halving problem. While recent work has shown that the approximate version of this problem is PPA-complete, we show that the exact version is much harder. Specifically, finding a solution ... More
Quantum hardness of learning shallow classical circuitsMar 07 2019In this paper we study the quantum learnability of constant-depth classical circuits under the uniform distribution and in the distribution-independent framework of PAC learning. In order to attain our results, we establish connections between quantum ... More
Closure of VP under taking factors: a short and simple proofMar 06 2019In this note, we give a short, simple and almost completely self contained proof of a classical result of Kaltofen [Kal86, Kal87, Kal89] which shows that if an $n$ variate degree $d$ polynomial $f$ can be computed by an arithmetic circuit of size $s$, ... More
Proving the NP-completeness of optimal moral graph triangulationMar 06 2019Moral graphs were introduced in the 1980s as an intermediate step when transforming a Bayesian network to a junction tree, on which exact belief propagation can be efficiently done. The moral graph of a Bayesian network can be trivially obtained by connecting ... More
Reducing the domination number of graphs via edge contractionsMar 05 2019In this paper, we study the following problem: given a connected graph $G$, can we reduce the domination number of $G$ by at least one using $k$ edge contractions, for some fixed integer $k \geq 0$? We present positive and negative results regarding the ... More
The Complexity of Morality: Checking Markov Blanket Consistency with DAGs via MoralityMar 05 2019A family of Markov blankets in a faithful Bayesian network satisfies the symmetry and consistency properties. In this paper, we draw a bijection between families of consistent Markov blankets and moral graphs. We define the new concepts of weak recursive ... More
Strongly Exponential Separation Between Monotone VP and Monotone VNPMar 05 2019We show that there is a sequence of explicit multilinear polynomials $P_n(x_1,\ldots,x_n)\in \mathbb{R}[x_1,\ldots,x_n]$ with non-negative coefficients that lies in monotone VNP such that any monotone algebraic circuit for $P_n$ must have size $\exp(\Omega(n)).$ ... More
Sign-Rank Can Increase Under IntersectionMar 01 2019The communication class $\mathbf{UPP}^{\text{cc}}$ is a communication analog of the Turing Machine complexity class $\mathbf{PP}$. It is characterized by a matrix-analytic complexity measure called sign-rank (also called dimension complexity), and is ... More
Efficient classical simulation of Clifford circuits with nonstabilizer input statesFeb 28 2019We investigate the problem of evaluating the output probabilities of Clifford circuits with nonstabilizer product input states. First, we consider the case when the input state is mixed, and give an efficient classical algorithm to approximate the output ... More
Interpretation of NDTM in the definition of NPFeb 28 2019In this paper, we interpret NDTM (NonDeterministic Turing Machine) used to define NP by tracing to the source of NP. Originally NP was defined as the class of problems solvable in polynomial time by a NDTM in the theorem of Cook, where the NDTM was represented ... More
Unifying computational entropies via Kullback-Leibler divergenceFeb 28 2019We introduce KL-hardness, a new notion of hardness for search problems which on the one hand is satisfied by all one-way functions and on the other hand implies both next-block pseudoentropy and inaccessible-entropy, two forms of computational entropy ... More
Dynamic Planar Convex HullFeb 28 2019In this article, we determine the amortized computational complexity of the planar dynamic convex hull problem by querying. We present a data structure that maintains a set of n points in the plane under the insertion and deletion of points in amortized ... More
A Hierarchy of Polynomial KernelsFeb 28 2019In parameterized algorithmics, the process of kernelization is defined as a polynomial time algorithm that transforms the instance of a given problem to an equivalent instance of a size that is limited by a function of the parameter. As, afterwards, this ... More
Lower Bounds for Multiplication via Network CodingFeb 28 2019Multiplication is one of the most fundamental computational problems, yet its true complexity remains elusive. The best known upper bound, by F\"{u}rer, shows that two $n$-bit numbers can be multiplied via a boolean circuit of size $O(n \lg n \cdot 4^{\lg^*n})$, ... More
Analysis of Quantum Multi-Prover Zero-Knowledge Systems: Elimination of the Honest Condition and Computational Zero-Knowledge Systems for QMIP*Feb 28 2019Zero-knowledge and multi-prover systems are both central notions in classical and quantum complexity theory. There is, however, little research in quantum multi-prover zero-knowledge systems. This paper studies complexity-theoretical aspects of the quantum ... More
An exponential lower bound for the degrees of invariants of cubic forms and tensor actionsFeb 27 2019Using the Grosshans Principle, we develop a method for proving lower bounds for the maximal degree of a system of generators of an invariant ring. This method also gives lower bounds for the maximal degree of a set of invariants that define Hilbert's ... More
Reconfiguration of Connected Graph PartitionsFeb 27 2019Motivated by recent computational models for redistricting and detection of gerrymandering, we study the following problem on graph partitions. Given a graph $G$ and an integer $k\geq 1$, a $k$-district map of $G$ is a partition of $V(G)$ into $k$ nonempty ... More
Algorithm and Hardness results on Liar's Dominating Set and $k$-tuple Dominating SetFeb 27 2019Given a graph $G=(V,E)$, the dominating set problem asks for a minimum subset of vertices $D\subseteq V$ such that every vertex $u\in V\setminus D$ is adjacent to at least one vertex $v\in D$. That is, the set $D$ satisfies the condition that $|N[v]\cap ... More
Linearly-growing Reductions of Karp's 21 NP-complete ProblemsFeb 27 2019We address the question of whether it may be worthwhile to convert certain, now classical, NP-complete problems to one of a smaller number of kernel NP-complete problems. In particular, we show that Karp's classical set of 21 NP-complete problems contains ... More
Decidability of the Mortality Problem: from multiplicative matrix equations to linear recurrence sequences and beyondFeb 26 2019We consider the following variant of the Mortality Problem: given $k\times k$ matrices $A_1, A_2, \dots,A_{t}$, does there exist nonnegative integers $m_1, m_2, \dots,m_t$ such that the product $A_1^{m_1} A_2^{m_2} \cdots A_{t}^{m_{t}}$ is equal to the ... More
On reachability problems for low dimensional matrix semigroupsFeb 25 2019We consider the Membership and the Half-space Reachability Problems for matrices in dimensions two and three. Our first main result is that the Membership Problem is decidable for fintely generated sub-semigroups of the Heisenberg group over integer numbers. ... More
Polynomially Ambiguous Probabilistic Automata on Restricted LanguagesFeb 25 2019We consider the computability and complexity of decision questions for Probabilistic Finite Automata (PFA) with sub-exponential ambiguity. We show that the emptiness problem for non strict cutpoints of polynomially ambiguous PFA remains undecidable even ... More