OpenRaiser/Intern-Atlas huggingface dataset:
READ-EVAL-PRINT in Parallel and Asynchronous Proof-checking
Venue: arXiv cs.LO 2013
Year: 2013

The LCF tradition of interactive theorem proving, which was started by Milner in the 1970-ies, appears to be tied to the classic READ-EVAL-PRINT-LOOP of sequential and synchronous evaluation of prover commands. We break up this loop and retrofit the read-eval-print phases into a model of parallel and asynchronous proof processing. Thus we explain some key concepts of the Isabelle/Scala approach to prover interaction and integration, and the Isabelle/jEdit Prover IDE as front-end technology. We hope to open up the scientific discussion about non-trivial interaction models for ITP systems again, and help getting other old-school proof assistants on a similar track.
Imperative Programs as Proofs via Game Semantics
Venue: arXiv cs.LO 2013
Year: 2013

Game semantics extends the Curry-Howard isomorphism to a three-way correspondence: proofs, programs, strategies. But the universe of strategies goes beyond intuitionistic logics and lambda calculus, to capture stateful programs. In this paper we describe a logical counterpart to this extension, in which proofs denote such strategies. The system is expressive: it contains all of the connectives of Intuitionistic Linear Logic, and first-order quantification. Use of Laird's sequoid operator allows proofs with imperative behaviour to be expressed. Thus, we can embed first-order Intuitionistic Linear Logic into this system, Polarized Linear Logic, and an imperative total programming language. The proof system has a tight connection with a simple game model, where games are forests of plays. Formulas are modelled as games, and proofs as history-sensitive winning strategies. We provide a strong full completeness result with respect to this model: each finitary strategy is the denotation of a unique analytic (cut-free) proof. Infinite strategies correspond to analytic proofs that are infinitely deep. Thus, we can normalise proofs, via the semantics.
Massively parallel solvers for elliptic PDEs in Numerical Weather- and Climate Prediction
Venue: arXiv cs.DC 2013
Year: 2013

The demand for substantial increases in the spatial resolution of global weather- and climate- prediction models makes it necessary to use numerically efficient and highly scalable algorithms to solve the equations of large scale atmospheric fluid dynamics. For stability and efficiency reasons several of the operational forecasting centres, in particular the Met Office and the ECMWF in the UK, use semi-implicit semi-Lagrangian time stepping in the dynamical core of the model. The additional burden with this approach is that a three dimensional elliptic partial differential equation (PDE) for the pressure correction has to be solved at every model time step and this often constitutes a significant proportion of the time spent in the dynamical core. To run within tight operational time scales the solver has to be parallelised and there seems to be a (perceived) misconception that elliptic solvers do not scale to large processor counts and hence implicit time stepping can not be used in very high resolution global models. After reviewing several methods for solving the elliptic PDE for the pressure correction and their application in atmospheric models we demonstrate the performance and very good scalability of Krylov subspace solvers and multigrid algorithms for a representative model equation with more than $10^{10}$ unknowns on 65536 cores on HECToR, the UK's national supercomputer. For this we tested and optimised solvers from two existing numerical libraries (DUNE and hypre) and implemented both a Conjugate Gradient solver and a geometric multigrid algorithm based on a tensor-product approach which exploits the strong vertical anisotropy of the discretised equation. We study both weak and strong scalability and compare the absolute solution times for all methods; in contrast to one-level methods the multigrid solver is robust with respect to parameter variations.
The benefit of law-making power
Venue: arXiv cs.GT 2013
Year: 2013

We study optimal equilibria in multi-player games. An equilibrium is optimal for a player, if her payoff is maximal. A tempting approach to solving this problem is to seek optimal Nash equilibria, the standard form of equilibria where no player has an incentive to deviate from her strategy. We argue that a player with the power to define an equilibrium is in a position, where she should not be interested in the symmetry of a Nash equilibrium, and ignore the question of whether or not her outcome can be improved if the other strategies are fixed. That is, she would only have to make sure that the other players have no incentive to deviate. This defines a greater class of equilibria, which may have better (and cannot have worse) optimal equilibria for the designated powerful player. We apply this strategy to concurrent bimatrix games and to turn based multi-player mean-payoff games. For the latter, we show that such political equilibria as well as Nash equilibria always exist, and provide simple examples where the political equilibrium is superior. We show that constructing political and Nash equilibria are NP-complete problems. We also show that, for a fixed number of players, the hardest part is to solve the underlying two-player mean-payoff games: using an MPG oracle, the problem is solvable in polynomial time. It is therefore in UP and CoUP, and can be solved in pseudo polynomial and expected subexponential time.
Computing the Fréchet distance with shortcuts is NP-hard
Venue: arXiv cs.CG 2013
Year: 2013

We study the shortcut Fréchet distance, a natural variant of the Fréchet distance, that allows us to take shortcuts from and to any point along one of the curves. The classic Fréchet distance is a bottle-neck distance measure and hence quite sensitive to outliers. The shortcut Fréchet distance allows us to cut across outliers and hence produces significantly more meaningful results when dealing with real world data. Driemel and Har-Peled recently described approximation algorithms for the restricted case where shortcuts have to start and end at input vertices. We show that, in the general case, the problem of computing the shortcut Fréchet distance is NP-hard. This is the first hardness result for a variant of the Fréchet distance between two polygonal curves in the plane. We also present two algorithms for the decision problem: a 3-approximation algorithm for the general case and an exact algorithm for the vertex-restricted case. Both algorithms run in O(n^3 log n) time.
Towards an Efficient Use of the BLAS Library for Multilinear Tensor Contractions
Venue: arXiv cs.MS 2013
Year: 2013

Mathematical operators whose transformation rules constitute the building blocks of a multi-linear algebra are widely used in physics and engineering applications where they are very often represented as tensors. In the last century, thanks to the advances in tensor calculus, it was possible to uncover new research fields and make remarkable progress in the existing ones, from electromagnetism to the dynamics of fluids and from the mechanics of rigid bodies to quantum mechanics of many atoms. By now, the formal mathematical and geometrical properties of tensors are well defined and understood; conversely, in the context of scientific and high-performance computing, many tensor- related problems are still open. In this paper, we address the problem of efficiently computing contractions among two tensors of arbitrary dimension by using kernels from the highly optimized BLAS library. In particular, we establish precise conditions to determine if and when GEMM, the kernel for matrix products, can be used. Such conditions take into consideration both the nature of the operation and the storage scheme of the tensors, and induce a classification of the contractions into three groups. For each group, we provide a recipe to guide the users towards the most effective use of BLAS.
Successive Integer-Forcing and its Sum-Rate Optimality
Venue: arXiv cs.IT 2013
Year: 2013

Integer-forcing receivers generalize traditional linear receivers for the multiple-input multiple-output channel by decoding integer-linear combinations of the transmitted streams, rather then the streams themselves. Previous works have shown that the additional degree of freedom in choosing the integer coefficients enables this receiver to approach the performance of maximum-likelihood decoding in various scenarios. Nonetheless, even for the optimal choice of integer coefficients, the additive noise at the equalizer's output is still correlated. In this work we study a variant of integer-forcing, termed successive integer-forcing, that exploits these noise correlations to improve performance. This scheme is the integer-forcing counterpart of successive interference cancellation for traditional linear receivers. Similarly to the latter, we show that successive integer-forcing is capacity achieving when it is possible to optimize the rate allocation to the different streams. In comparison to standard successive interference cancellation receivers, the successive integer-forcing receiver offers more possibilities for capacity achieving rate tuples, and in particular, ones that are more balanced.
Near-Optimal Encoding for Sigma-Delta Quantization of Finite Frame Expansions
Venue: arXiv cs.IT 2013
Year: 2013

In this paper we investigate encoding the bit-stream resulting from coarse Sigma-Delta quantization of finite frame expansions (i.e., overdetermined representations) of vectors. We show that for a wide range of finite-frames, including random frames and piecewise smooth frames, there exists a simple encoding algorithm ---acting only on the Sigma-Delta bit stream--- and an associated decoding algorithm that together yield an approximation error which decays exponentially in the number of bits used. The encoding strategy consists of applying a discrete random operator to the Sigma-Delta bit stream and assigning a binary codeword to the result. The reconstruction procedure is essentially linear and equivalent to solving a least squares minimization problem.
Combinatorial decomposition approaches for efficient counting and random generation FPTASes
Venue: arXiv cs.DS 2013
Year: 2013

Given a combinatorial decomposition for a counting problem, we resort to the simple scheme of approximating large numbers by floating-point representations in order to obtain efficient Fully Polynomial Time Approximation Schemes (FPTASes) for it. The number of bits employed for the exponent and the mantissa will depend on the error parameter $0 < \varepsilon \leq 1$ and on the characteristics of the problem. Accordingly, we propose the first FPTASes with $1 \pm \varepsilon$ relative error for counting and generating uniformly at random a labeled DAG with a given number of vertices. This is accomplished starting from a classical recurrence for counting DAGs, whose values we approximate by floating-point numbers. After extending these results to other families of DAGs, we show how the same approach works also with problems where we are given a compact representation of a combinatorial ensemble and we are asked to count and sample elements from it. We employ here the floating-point approximation method to transform the classic pseudo-polynomial algorithm for counting 0/1 Knapsack solutions into a very simple FPTAS with $1 - \varepsilon$ relative error. Its complexity improves upon the recent result (Štefankovič et al., SIAM J. Comput., 2012), and, when $\varepsilon^{-1} = Ω(n)$, also upon the best-known randomized algorithm (Dyer, STOC, 2003). To show the versatility of this technique, we also apply it to a recent generalization of the problem of counting 0/1 Knapsack solutions in an arc-weighted DAG, obtaining a faster and simpler FPTAS than the existing one.
On the $μ$-parameters of the Petersen graph
Venue: arXiv cs.DM 2013
Year: 2013

For an undirected, simple, finite, connected graph $G$, we denote by $V(G)$ and $E(G)$ the sets of its vertices and edges, respectively. A function $φ:E(G)\rightarrow \{1,...,t\}$ is called a proper edge $t$-coloring of a graph $G$, if adjacent edges are colored differently and each of $t$ colors is used. The least value of $t$ for which there exists a proper edge $t$-coloring of a graph $G$ is denoted by $χ'(G)$. For any graph $G$, and for any integer $t$ satisfying the inequality $χ'(G)\leq t\leq |E(G)|$, we denote by $α(G,t)$ the set of all proper edge $t$-colorings of $G$. Let us also define a set $α(G)$ of all proper edge colorings of a graph $G$: $$ α(G)\equiv\bigcup_{t=χ'(G)}^{|E(G)|}α(G,t). $$ An arbitrary nonempty finite subset of consecutive integers is called an interval. If $φ\inα(G)$ and $x\in V(G)$, then the set of colors of edges of $G$ which are incident with $x$ is denoted by $S_G(x,φ)$ and is called a spectrum of the vertex $x$ of the graph $G$ at the proper edge coloring $φ$. If $G$ is a graph and $φ\inα(G)$, then define $f_G(φ)\equiv|\{x\in V(G)/S_G(x,φ) \textrm{is an interval}\}|$. For a graph $G$ and any integer $t$, satisfying the inequality $χ'(G)\leq t\leq |E(G)|$, we define: $$ μ_1(G,t)\equiv\min_{φ\inα(G,t)}f_G(φ),\qquad μ_2(G,t)\equiv\max_{φ\inα(G,t)}f_G(φ). $$ For any graph $G$, we set: $$ μ_{11}(G)\equiv\min_{χ'(G)\leq t\leq|E(G)|}μ_1(G,t),\qquad μ_{12}(G)\equiv\max_{χ'(G)\leq t\leq|E(G)|}μ_1(G,t), $$ $$ μ_{21}(G)\equiv\min_{χ'(G)\leq t\leq|E(G)|}μ_2(G,t),\qquad μ_{22}(G)\equiv\max_{χ'(G)\leq t\leq|E(G)|}μ_2(G,t). $$ For the Petersen graph, the exact values of the parameters $μ_{11}$, $μ_{12}$, $μ_{21}$ and $μ_{22}$ are found.
Major Limitations of Satellite images
Venue: arXiv cs.CV 2013
Year: 2013

Remote sensing has proven to be a powerful tool for the monitoring of the Earth surface to improve our perception of our surroundings has led to unprecedented developments in sensor and information technologies. However, technologies for effective use of the data and for extracting useful information from the data of Remote sensing are still very limited since no single sensor combines the optimal spectral, spatial and temporal resolution. This paper briefly reviews the limitations of satellite remote sensing. Also, reviews on the problems of image fusion techniques. The conclusion of this, According to literature, the remote sensing is still the lack of software tools for effective information extraction from remote sensing data. The trade-off in spectral and spatial resolution will remain and new advanced data fusion approaches are needed to make optimal use of remote sensors for extract the most useful information.
Abstract GSOS Rules and a Modular Treatment of Recursive Definitions
Venue: arXiv cs.LO 2013
Year: 2013

Terminal coalgebras for a functor serve as semantic domains for state-based systems of various types. For example, behaviors of CCS processes, streams, infinite trees, formal languages and non-well-founded sets form terminal coalgebras. We present a uniform account of the semantics of recursive definitions in terminal coalgebras by combining two ideas: (1) abstract GSOS rules l specify additional algebraic operations on a terminal coalgebra; (2) terminal coalgebras are also initial completely iterative algebras (cias). We also show that an abstract GSOS rule leads to new extended cia structures on the terminal coalgebra. Then we formalize recursive function definitions involving given operations specified by l as recursive program schemes for l, and we prove that unique solutions exist in the extended cias. From our results it follows that the solutions of recursive (function) definitions in terminal coalgebras may be used in subsequent recursive definitions which still have unique solutions. We call this principle modularity. We illustrate our results by the five concrete terminal coalgebras mentioned above, e.\,g., a finite stream circuit defines a unique stream function.
Exploiting Data Parallelism in the yConvex Hypergraph Algorithm for Image Representation using GPGPUs
Venue: arXiv cs.DC 2013
Year: 2013

To define and identify a region-of-interest (ROI) in a digital image, the shape descriptor of the ROI has to be described in terms of its boundary characteristics. To address the generic issues of contour tracking, the yConvex Hypergraph (yCHG) model was proposed by Kanna et al [1]. In this work, we propose a parallel approach to implement the yCHG model by exploiting massively parallel cores of NVIDIA's Compute Unified Device Architecture (CUDA). We perform our experiments on the MODIS satellite image database by NASA, and based on our analysis we observe that the performance of the serial implementation is better on smaller images, but once the threshold is achieved in terms of image resolution, the parallel implementation outperforms its sequential counterpart by 2 to 10 times (2x-10x). We also conclude that an increase in the number of hyperedges in the ROI of a given size does not impact the performance of the overall algorithm.
Priced Timed Petri Nets
Venue: arXiv cs.LO 2013
Year: 2013

We consider priced timed Petri nets, i.e., unbounded Petri nets where each token carries a real-valued clock. Transition arcs are labeled with time intervals, which specify constraints on the ages of tokens. Furthermore, our cost model assigns token storage costs per time unit to places, and firing costs to transitions. This general model strictly subsumes both priced timed automata and unbounded priced Petri nets. We study the cost of computations that reach a given control-state. In general, a computation with minimal cost may not exist, due to strict inequalities in the time constraints. However, we show that the infimum of the costs to reach a given control-state is computable in the case where all place and transition costs are non-negative. On the other hand, if negative costs are allowed, then the question whether a given control-state is reachable with zero overall cost becomes undecidable. In fact, this negative result holds even in the simpler case of discrete time (i.e., integer-valued clocks).
Towards an Approach for Analysing the Strategic Alignment of Software Requirements using Quantified Goal Graphs
Venue: arXiv cs.SE 2013
Year: 2013

Analysing the strategic alignment of software requirements primarily provides assurance to stakeholders that the software-to-be will add value to the organisation. Additionally, such analysis can improve a requirement by disambiguating its purpose and value, thereby supporting validation and value-oriented decisions in requirements engineering processes, such as prioritisation, release planning, and trade-off analysis. We review current approaches that could enable such an analysis. We focus on Goal Oriented Requirements Engineering methodologies, since goal graphs are well suited for relating software goals to business goals. However, we argue that unless the extent of goal-goal contribution is quantified with verifiable metrics, goal graphs are not sufficient for demonstrating the strategic alignment of software requirements. Since the concept of goal contribution is predictive, what results is a forecast of the benefits of implementing software requirements. Thus, we explore how the description of the contribution relationship can be enriched with concepts such as uncertainty and confidence, non-linear causation, and utility. We introduce the approach using an example software project from Rolls-Royce.
Ontology Based Data Integration Over Document and Column Family Oriented NOSQL
Venue: arXiv cs.DB 2013
Year: 2013

The World Wide Web infrastructure together with its more than 2 billion users enables to store information at a rate that has never been achieved before. This is mainly due to the will of storing almost all end-user interactions performed on some web applications. In order to reply to scalability and availability constraints, many web companies involved in this process recently started to design their own data management systems. Many of them are referred to as NOSQL databases, standing for 'Not only SQL'. With their wide adoption emerges new needs and data integration is one of them. In this paper, we consider that an ontology-based representation of the information stored in a set of NOSQL sources is highly needed. The main motivation of this approach is the ability to reason on elements of the ontology and to retrieve information in an efficient and distributed manner. Our contributions are the following: (1) we analyze a set of schemaless NOSQL databases to generate local ontologies, (2) we generate a global ontology based on the discovery of correspondences between the local ontologies and finally (3) we propose a query translation solution from SPARQL to query languages of the sources. We are currently implementing our data integration solution on two popular NOSQL databases: MongoDB as a document database and Cassandra as a column family store.
Ranking on Arbitrary Graphs: Rematch via Continuous LP with Monotone and Boundary Condition Constraints
Venue: arXiv cs.DS 2013
Year: 2013

Motivated by online advertisement and exchange settings, greedy randomized algorithms for the maximum matching problem have been studied, in which the algorithm makes (random) decisions that are essentially oblivious to the input graph. Any greedy algorithm can achieve performance ratio 0.5, which is the expected number of matched nodes to the number of nodes in a maximum matching. Since Aronson, Dyer, Frieze and Suen proved that the Modified Randomized Greedy (MRG) algorithm achieves performance ratio 0.5 + ε(where ε= frac{1}{400000}) on arbitrary graphs in the mid-nineties, no further attempts in the literature have been made to improve this theoretical ratio for arbitrary graphs until two papers were published in FOCS 2012. Poloczek and Szegedy also analyzed the MRG algorithm to give ratio 0.5039, while Goel and Tripathi used experimental techniques to analyze the Ranking algorithm to give ratio 0.56. However, we could not reproduce the experimental results of Goel and Tripathi. In this paper, we revisit the Ranking algorithm using the LP framework. Special care is given to analyze the structural properties of the Ranking algorithm in order to derive the LP constraints, of which one known as the \emph{boundary} constraint requires totally new analysis and is crucial to the success of our LP. We use continuous LP relaxation to analyze the limiting behavior as the finite LP grows. Of particular interest are new duality and complementary slackness characterizations that can handle the monotone and the boundary constraints in continuous LP. We believe our work achieves the currently best theoretical performance ratio of \frac{2(5-\sqrt{7})}{9} \approx 0.523 on arbitrary graphs. Moreover, experiments suggest that Ranking cannot perform better than 0.724 in general.
Positivity Problems for Low-Order Linear Recurrence Sequences
Venue: arXiv cs.DM 2013
Year: 2013

We consider two decision problems for linear recurrence sequences (LRS) over the integers, namely the Positivity Problem (are all terms of a given LRS positive?) and the Ultimate Positivity Problem} (are all but finitely many terms of a given LRS positive?). We show decidability of both problems for LRS of order 5 or less, with complexity in the Counting Hierarchy for Positivity, and in polynomial time for Ultimate Positivity. Moreover, we show by way of hardness that extending the decidability of either problem to LRS of order 6 would entail major breakthroughs in analytic number theory, more precisely in the field of Diophantine approximation of transcendental numbers.
A Hybrid ARQ Scheme Based on Polar Codes
Venue: arXiv cs.IT 2013
Year: 2013

A hybrid automatic repeat request (HARQ) scheme based on a novel class of rate-compatible polar (\mbox{RCP}) codes are proposed. The RCP codes are constructed by performing punctures and repetitions on the conventional polar codes. Simulation results over binary-input additive white Gaussian noise channels (BAWGNCs) show that, using a low-complexity successive cancellation (SC) decoder, the proposed HARQ scheme performs as well as the existing schemes based on turbo codes and low-density parity-check (LDPC) codes. The proposed transmission scheme is only about 1.0-1.5dB away from the channel capacity with the information block length of 1024 bits.