OpenRaiser/Intern-Atlas huggingface dataset:
Achieving New Upper Bounds for the Hypergraph Duality Problem through Logic
Venue: arXiv cs.CC 2017
Year: 2017

The hypergraph duality problem DUAL is defined as follows: given two simple hypergraphs $\mathcal{G}$ and $\mathcal{H}$, decide whether $\mathcal{H}$ consists precisely of all minimal transversals of $\mathcal{G}$ (in which case we say that $\mathcal{G}$ is the dual of $\mathcal{H}$). This problem is equivalent to deciding whether two given non-redundant monotone DNFs are dual. It is known that non-DUAL, the complementary problem to DUAL, is in $\mathrm{GC}(\log^2 n,\mathrm{PTIME})$, where $\mathrm{GC}(f(n),\mathcal{C})$ denotes the complexity class of all problems that after a nondeterministic guess of $O(f(n))$ bits can be decided (checked) within complexity class $\mathcal{C}$. It was conjectured that non-DUAL is in $\mathrm{GC}(\log^2 n,\mathrm{LOGSPACE})$. In this paper we prove this conjecture and actually place the non-DUAL problem into the complexity class $\mathrm{GC}(\log^2 n,\mathrm{TC}^0)$ which is a subclass of $\mathrm{GC}(\log^2 n,\mathrm{LOGSPACE})$. We here refer to the logtime-uniform version of $\mathrm{TC}^0$, which corresponds to $\mathrm{FO(COUNT)}$, i.e., first order logic augmented by counting quantifiers. We achieve the latter bound in two steps. First, based on existing problem decomposition methods, we develop a new nondeterministic algorithm for non-DUAL that requires to guess $O(\log^2 n)$ bits. We then proceed by a logical analysis of this algorithm, allowing us to formulate its deterministic part in $\mathrm{FO(COUNT)}$. From this result, by the well known inclusion $\mathrm{TC}^0\subseteq\mathrm{LOGSPACE}$, it follows that DUAL belongs also to $\mathrm{DSPACE}[\log^2 n]$. Finally, by exploiting the principles on which the proposed nondeterministic algorithm is based, we devise a deterministic algorithm that, given two hypergraphs $\mathcal{G}$ and $\mathcal{H}$, computes in quadratic logspace a transversal of $\mathcal{G}$ missing in $\mathcal{H}$.
Partial Quantifier Elimination
Venue: arXiv cs.LO 2017
Year: 2017

We consider the problem of Partial Quantifier Elimination (PQE). Given formula exists(X)[F(X,Y) & G(X,Y)], where F, G are in conjunctive normal form, the PQE problem is to find a formula F*(Y) such that F* & exists(X)[G] is logically equivalent to exists(X)[F & G]. We solve the PQE problem by generating and adding to F clauses over the free variables that make the clauses of F with quantified variables redundant. The traditional Quantifier Elimination problem (QE) is a special case of PQE where G is empty so all clauses of the input formula with quantified variables need to be made redundant. The importance of PQE is twofold. First, many problems are more naturally formulated in terms of PQE rather than QE. Second, in many cases PQE can be solved more efficiently than QE. We describe a PQE algorithm based on the machinery of dependency sequents and give experimental results showing the promise of PQE.
Cooperative Game Theoretic Solution Concepts for top-$k$ Problems
Venue: arXiv cs.SI 2017
Year: 2017

The problem of finding the $k$ most critical nodes, referred to as the $top\text{-}k$ problem, is a very important one in several contexts such as information diffusion and preference aggregation in social networks, clustering of data points, etc. It has been observed in the literature that the value allotted to a node by most of the popular cooperative game theoretic solution concepts, acts as a good measure of appropriateness of that node (or a data point) to be included in the $top\text{-}k$ set, by itself. However, in general, nodes having the highest $k$ values are not the desirable $top\text{-}k$ nodes, because the appropriateness of a node to be a part of the $top\text{-}k$ set depends on other nodes in the set. As this is not explicitly captured by cooperative game theoretic solution concepts, it is necessary to post-process the obtained values in order to output the suitable $top\text{-}k$ nodes. In this paper, we propose several such post-processing methods and give reasoning behind each of them, and also propose a standalone algorithm that combines cooperative game theoretic solution concepts with the popular greedy hill-climbing algorithm.
New Trends in Parallel and Distributed Simulation: from Many-Cores to Cloud Computing
Venue: arXiv cs.DC 2017
Year: 2017

Recent advances in computing architectures and networking are bringing parallel computing systems to the masses so increasing the number of potential users of these kinds of systems. In particular, two important technological evolutions are happening at the ends of the computing spectrum: at the "small" scale, processors now include an increasing number of independent execution units (cores), at the point that a mere CPU can be considered a parallel shared-memory computer; at the "large" scale, the Cloud Computing paradigm allows applications to scale by offering resources from a large pool on a pay-as-you-go model. Multi-core processors and Clouds both require applications to be suitably modified to take advantage of the features they provide. In this paper, we analyze the state of the art of parallel and distributed simulation techniques, and assess their applicability to multi-core architectures or Clouds. It turns out that most of the current approaches exhibit limitations in terms of usability and adaptivity which may hinder their application to these new computing architectures. We propose an adaptive simulation mechanism, based on the multi-agent system paradigm, to partially address some of those limitations. While it is unlikely that a single approach will work well on both settings above, we argue that the proposed adaptive mechanism has useful features which make it attractive both in a multi-core processor and in a Cloud system. These features include the ability to reduce communication costs by migrating simulation components, and the support for adding (or removing) nodes to the execution architecture at runtime. We will also show that, with the help of an additional support layer, parallel and distributed simulations can be executed on top of unreliable resources.
Designing labeled graph classifiers by exploiting the Rényi entropy of the dissimilarity representation
Venue: arXiv cs.CV 2017
Year: 2017

Representing patterns as labeled graphs is becoming increasingly common in the broad field of computational intelligence. Accordingly, a wide repertoire of pattern recognition tools, such as classifiers and knowledge discovery procedures, are nowadays available and tested for various datasets of labeled graphs. However, the design of effective learning procedures operating in the space of labeled graphs is still a challenging problem, especially from the computational complexity viewpoint. In this paper, we present a major improvement of a general-purpose classifier for graphs, which is conceived on an interplay between dissimilarity representation, clustering, information-theoretic techniques, and evolutionary optimization algorithms. The improvement focuses on a specific key subroutine devised to compress the input data. We prove different theorems which are fundamental to the setting of the parameters controlling such a compression operation. We demonstrate the effectiveness of the resulting classifier by benchmarking the developed variants on well-known datasets of labeled graphs, considering as distinct performance indicators the classification accuracy, computing time, and parsimony in terms of structural complexity of the synthesized classification models. The results show state-of-the-art standards in terms of test set accuracy and a considerable speed-up for what concerns the computing time.
Weight distribution of cosets of small codes with good dual properties
Venue: arXiv cs.IT 2017
Year: 2017

The bilateral minimum distance of a binary linear code is the maximum $d$ such that all nonzero codewords have weights between $d$ and $n-d$. Let $Q\subset \{0,1\}^n$ be a binary linear code whose dual has bilateral minimum distance at least $d$, where $d$ is odd. Roughly speaking, we show that the average $L_\infty$-distance -- and consequently the $L_1$-distance -- between the weight distribution of a random cosets of $Q$ and the binomial distribution decays quickly as the bilateral minimum distance $d$ of the dual of $Q$ increases. For $d = Θ(1)$, it decays like $n^{-Θ(d)}$. On the other $d=Θ(n)$ extreme, it decays like and $e^{-Θ(d)}$. It follows that, almost all cosets of $Q$ have weight distributions very close to the to the binomial distribution. In particular, we establish the following bounds. If the dual of $Q$ has bilateral minimum distance at least $d=2t+1$, where $t\geq 1$ is an integer, then the average $L_\infty$-distance is at most $\min\{\left(e\ln{\frac{n}{2t}}\right)^{t}\left(\frac{2t}{n}\right)^{\frac{t}{2} }, \sqrt{2} e^{-\frac{t}{10}}\}$. For the average $L_1$-distance, we conclude the bound $\min\{(2t+1)\left(e\ln{\frac{n}{2t}}\right)^{t} \left(\frac{2t}{n}\right)^{\frac{t}{2}-1},\sqrt{2}(n+1)e^{-\frac{t}{10}}\}$, which gives nontrivial results for $t\geq 3$. We given applications to the weight distribution of cosets of extended Hadamard codes and extended dual BCH codes. Our argument is based on Fourier analysis, linear programming, and polynomial approximation techniques.
On the Continuity of the Secrecy Capacity of Compound and Arbitrarily Varying Wiretap Channels
Venue: arXiv cs.IT 2017
Year: 2017

The wiretap channel models secure communication between two users in the presence of an eavesdropper who must be kept ignorant of transmitted messages. The performance of such a system is usually characterized by its secrecy capacity which determines the maximum transmission rate of secure communication. In this paper, the issue of whether or not the secrecy capacity is a continuous function of the system parameters is examined. In particular, this is done for channel uncertainty modeled via compound channels and arbitrarily varying channels, in which the legitimate users know only that the true channel realization is from a pre-specified uncertainty set. In the former model, this realization remains constant for the entire duration of transmission, while in the latter the realization varies from channel use to channel use in an unknown and arbitrary manner. These models not only capture the case of channel uncertainty, but are also suitable for modeling scenarios in which a malicious adversary jams or otherwise influence the legitimate transmission. The secrecy capacity of the compound wiretap channel is shown to be robust in the sense that it is a continuous function of the uncertainty set. Thus, small variations in the uncertainty set lead to small variations in secrecy capacity. On the other hand, the deterministic secrecy capacity of the \emph{arbitrarily varying wiretap channel} is shown to be discontinuous in the uncertainty set meaning that small variations can lead to dramatic losses in capacity.
Inferring Object Properties with a Tactile Sensing Array Given Varying Joint Stiffness and Velocity
Venue: arXiv cs.RO 2017
Year: 2017

Whole-arm tactile sensing enables a robot to sense contact and infer contact properties across its entire arm. Within this paper, we demonstrate that using data-driven methods, a humanoid robot can infer mechanical properties of objects from contact with its forearm during a simple reaching motion. A key issue is the extent to which the performance of data-driven methods can generalize to robot actions that differ from those used during training. To investigate this, we developed an idealized physics-based lumped element model of a robot with a compliant joint making contact with an object. Using this physics-based model, we performed experiments with varied robot, object and environment parameters. We also collected data from a tactile-sensing forearm on a real robot as it made contact with various objects during a simple reaching motion with varied arm velocities and joint stiffnesses. The robot used one nearest neighbor classifiers (1-NN), hidden Markov models (HMMs), and long short-term memory (LSTM) networks to infer two object properties (hard vs. soft and moved vs. unmoved) based on features of time-varying tactile sensor data (maximum force, contact area, and contact motion). We found that, in contrast to 1-NN, the performance of LSTMs (with sufficient data availability) and multivariate HMMs successfully generalized to new robot motions with distinct velocities and joint stiffnesses. Compared to single features, using multiple features gave the best results for both experiments with physics-based models and a real-robot.
Cyclic Codes over the Matrix Ring $M_2(F_p)$ and Their Isometric Images over $F_{p^2}+uF_{p^2}$
Venue: arXiv cs.IT 2017
Year: 2017

Let $F_p$ be the prime field with $p$ elements. We derive the homogeneous weight on the Frobenius matrix ring $M_2(F_p)$ in terms of the generating character. We also give a generalization of the Lee weight on the finite chain ring $F_{p^2}+uF_{p^2}$ where $u^2=0$. A non-commutative ring, denoted by $\mathcal{F}_{p^2}+\mathbf{v}_p \mathcal{F}_{p^2}$, $\mathbf{v}_p$ an involution in $M_2(F_p)$, that is isomorphic to $M_2(F_p)$ and is a left $F_{p^2}$-vector space, is constructed through a unital embedding $τ$ from $F_{p^2}$ to $M_2(F_p)$. The elements of $\mathcal{F}_{p^2}$ come from $M_2(F_p)$ such that $τ(F_{p^2})=\mathcal{F}_{p^2}$. The irreducible polynomial $f(x)=x^2+x+(p-1) \in F_p[x]$ required in $τ$ restricts our study of cyclic codes over $M_2(F_p)$ endowed with the Bachoc weight to the case $p\equiv$ $2$ or $3$ mod $5$. The images of these codes via a left $F_p$-module isometry are additive cyclic codes over $F_{p^2}+uF_{p^2}$ endowed with the Lee weight. New examples of such codes are given.
The Minimum Feasible Tileset problem
Venue: arXiv cs.CC 2017
Year: 2017

We introduce and study the Minimum Feasible Tileset problem: Given a set of symbols and subsets of these symbols (scenarios), find a smallest possible number of pairs of symbols (tiles) such that each scenario can be formed by selecting at most one symbol from each tile. We show that this problem is APX-hard and that it is NP-hard even if each scenario contains at most three symbols. Our main result is a 4/3-approximation algorithm for the general case. In addition, we show that the Minimum Feasible Tileset problem is fixed-parameter tractable both when parameterized with the number of scenarios and with the number of symbols.
Naive Bayes and Text Classification I - Introduction and Theory
Venue: arXiv cs.LG 2017
Year: 2017

Naive Bayes classifiers, a family of classifiers that are based on the popular Bayes' probability theorem, are known for creating simple yet well performing models, especially in the fields of document classification and disease prediction. In this article, we will look at the main concepts of naive Bayes classification in the context of document categorization.
Minimisation of Multiplicity Tree Automata
Venue: arXiv cs.FL 2017
Year: 2017

We consider the problem of minimising the number of states in a multiplicity tree automaton over the field of rational numbers. We give a minimisation algorithm that runs in polynomial time assuming unit-cost arithmetic. We also show that a polynomial bound in the standard Turing model would require a breakthrough in the complexity of polynomial identity testing by proving that the latter problem is logspace equivalent to the decision version of minimisation. The developed techniques also improve the state of the art in multiplicity word automata: we give an NC algorithm for minimising multiplicity word automata. Finally, we consider the minimal consistency problem: does there exist an automaton with $n$ states that is consistent with a given finite sample of weight-labelled words or trees? We show that this decision problem is complete for the existential theory of the rationals, both for words and for trees of a fixed alphabet rank.
Exact Expression For Information Distance
Venue: arXiv cs.IT 2017
Year: 2017

Information distance can be defined not only between two strings but also in a finite multiset of strings of cardinality greater than two. We give an elementary proof for expressing the information distance in terms of plain Kolmogorov complexity. It is exact since for each cardinality of the multiset the lower bound for some multiset equals the upper bound for all multisets up to a constant additive term.
Robust Piecewise-Constant Smoothing: M-Smoother Revisited
Venue: arXiv cs.CV 2017
Year: 2017

A robust estimator, namely M-smoother, for piecewise-constant smoothing is revisited in this paper. Starting from its generalized formulation, we propose a numerical scheme/framework for solving it via a series of weighted-average filtering (e.g., box filtering, Gaussian filtering, bilateral filtering, and guided filtering). Because of the equivalence between M-smoother and local-histogram-based filters (such as median filter and mode filter), the proposed framework enables fast approximation of histogram filters via a number of box filtering or Gaussian filtering. In addition, high-quality piecewise-constant smoothing can be achieved via a number of bilateral filtering or guided filtering integrated in the proposed framework. Experiments on depth map denoising show the effectiveness of our framework.
A Generative Model of Software Dependency Graphs to Better Understand Software Evolution
Venue: arXiv cs.SE 2017
Year: 2017

Software systems are composed of many interacting elements. A natural way to abstract over software systems is to model them as graphs. In this paper we consider software dependency graphs of object-oriented software and we study one topological property: the degree distribution. Based on the analysis of ten software systems written in Java, we show that there exists completely different systems that have the same degree distribution. Then, we propose a generative model of software dependency graphs which synthesizes graphs whose degree distribution is close to the empirical ones observed in real software systems. This model gives us novel insights on the potential fundamental rules of software evolution.
A Framework for Transceiver Designs for Multi-Hop Communications with Covariance Shaping Constraints
Venue: arXiv cs.IT 2017
Year: 2017

For multiple-input multiple-output (MIMO) transceiver designs, sum power constraint is an elegant and ideal model. When various practical limitations are taken into account e.g., peak power constraints, per-antenna power constraints, etc., covariance shaping constraints will act as an effective and reasonable model. In this paper, we develop a framework for transceiver designs for multi-hop communications under covariance shaping constraints. Particularly, we focus on multi-hop amplify-and-forward (AF) MIMO relaying communications which are recognized as a key enabling technology for device-to-device (D2D) communications for next generation wireless systems such as 5G. The proposed framework includes a broad range of various linear and nonlinear transceiver designs as its special cases. It reveals an interesting fact that the relaying operation in each hop can be understood as a matrix version weighting operation. Furthermore, the nonlinear operations of Tomolision-Harashima Precoding (THP) and Decision Feedback Equalizer (DFE) also belong to the category of this kind of matrix version weighting operation. Furthermore, for both the cases with only pure shaping constraints or joint power constraints, the closed-form optimal solutions have been derived. At the end of this paper, the performance of the various designs is assessed by simulations.
Program Logics for Homogeneous Generative Run-Time Meta-Programming
Venue: arXiv cs.LO 2017
Year: 2017

This paper provides the first program logic for homogeneous generative run-time meta-programming---using a variant of MiniML by Davies and Pfenning as its underlying meta-programming language. We show the applicability of our approach by reasoning about example meta-programs from the literature. We also demonstrate that our logics are relatively complete in the sense of Cook, enable the inductive derivation of characteristic formulae, and exactly capture the observational properties induced by the operational semantics.
Quantum Invariants of 3-manifolds and NP vs #P
Venue: arXiv cs.CC 2017
Year: 2017

The computational complexity class #P captures the difficulty of counting the satisfying assignments to a boolean formula. In this work, we use basic tools from quantum computation to give a proof that the SO(3) Witten-Reshetikhin-Turaev (WRT) invariant of 3-manifolds is #P-hard to calculate. We then apply this result to a question about the combinatorics of Heegaard splittings, motivated by analogous work on link diagrams by M. Freedman. We show that, if $\#\text{P}\neq\text{FP}^\text{NP}$, then there exist infinitely many Heegaard splittings which cannot be made logarithmically thin by local WRT-preserving moves, except perhaps via a superpolynomial number of steps. We also outline two extensions of the above results. First, adapting a result of Kuperberg, we show that any presentation-independent approximation of WRT is also #P-hard. Second, we sketch out how all of our results can be translated to the setting of triangulations and Turaev-Viro invariants.
Complexity of Secure Sets
Venue: arXiv cs.CC 2017
Year: 2017

A secure set $S$ in a graph is defined as a set of vertices such that for any $X\subseteq S$ the majority of vertices in the neighborhood of $X$ belongs to $S$. It is known that deciding whether a set $S$ is secure in a graph is co-NP-complete. However, it is still open how this result contributes to the actual complexity of deciding whether for a given graph $G$ and integer $k$, a non-empty secure set for $G$ of size at most $k$ exists. In this work, we pinpoint the complexity of this problem by showing that it is $Σ^P_2$-complete. Furthermore, the problem has so far not been subject to a parameterized complexity analysis that considers structural parameters. In the present work, we prove that the problem is $W[1]$-hard when parameterized by treewidth. This is surprising since the problem is known to be FPT when parameterized by solution size and "subset problems" that satisfy this property usually tend to be FPT for bounded treewidth as well. Finally, we give an upper bound by showing membership in XP, and we provide a positive result in the form of an FPT algorithm for checking whether a given set is secure on graphs of bounded treewidth.
Data Generation for Testing and Grading SQL Queries
Venue: arXiv cs.DB 2017
Year: 2017

Correctness of SQL queries is usually tested by executing the queries on one or more datasets. Erroneous queries are often the results of small changes, or mutations of the correct query. A mutation Q' of a query Q is killed by a dataset D if Q(D) $\neq$ Q'(D). Earlier work on the XData system showed how to generate datasets that kill all mutations in a class of mutations that included join type and comparison operation mutations. In this paper, we extend the XData data generation techniques to handle a wider variety of SQL queries and a much larger class of mutations. We have also built a system for grading SQL queries using the datasets generated by XData. We present a study of the effectiveness of the datasets generated by the extended XData approach, using a variety of queries including queries submitted by students as part of a database course. We show that the XData datasets outperform predefined datasets as well as manual grading done earlier by teaching assistants, while also avoiding the drudgery of manual correction. Thus, we believe that our techniques will be of great value to database course instructors and TAs, particularly to those of MOOCs. It will also be valuable to database application developers and testers for testing SQL queries.