ConSUS: A light-weight program conditioner

Program conditioning consists of identifying and removing a set of statements which cannot be executed when a condition of interest holds at some point in a program. It has been applied to problems in maintenance, testing, re-use and re-engineering. All current approaches to program conditioning rely upon both symbolic execution and reasoning about symbolic predicates. The reasoning can be performed by a ‘heavy duty’ theorem prover but this may impose unrealistic performance constraints. This paper reports on a lightweight approach to theorem proving using the FermaT Simplify decision procedure. This is used as a component to ConSUS, a program conditioning system for the Wide Spectrum Language WSL. The paper describes the symbolic execution algorithm used by ConSUS, which prunes as it conditions. The paper also provides empirical evidence that conditioning produces a significant reduction in program size and, although exponential in the worst case, the conditioning system has low degree polynomial behaviour in many cases, thereby making it scalable to unit level applications of program conditioning

Blind Construction of Optimal Nonlinear Recursive Predictors for Discrete Sequences

We present a new method for nonlinear prediction of discrete random sequences under minimal structural assumptions. We give a mathematical construction for optimal predictors of such processes, in the form of hidden Markov models. We then describe an algorithm, CSSR (Causal-State Splitting Reconstruction), which approximates the ideal predictor from data. We discuss the reliability of CSSR, its data requirements, and its performance in simulations. Finally, we compare our approach to existing methods using variable-length Markov models and cross-validated hidden Markov models, and show theoretically and experimentally that our method delivers results superior to the former and at least comparable to the latter.Comment: 8 pages, 4 figure

Circuit models and SPICE macro-models for quantum Hall effect devices

Quantum Hall effect (QHE) devices are a pillar of modern quantum electrical metrology. Electrical networks including one or more QHE elements can be used as quantum resistance and impedance standards. The analysis of these networks allows metrologists to evaluate the effect of the inevitable parasitic parameters on their performance as standards. This paper presents a systematic analysis of the various circuit models for QHE elements proposed in the literature, and the development of a new model. This last model is particularly suited to be employed with the analogue electronic circuit simulator SPICE. The SPICE macro-model and examples of SPICE simulations, validated by comparison with the corresponding analytical solution and/or experimental data, are provided

Towards Model Checking Real-World Software-Defined Networks (version with appendix)

In software-defined networks (SDN), a controller program is in charge of deploying diverse network functionality across a large number of switches, but this comes at a great risk: deploying buggy controller code could result in network and service disruption and security loopholes. The automatic detection of bugs or, even better, verification of their absence is thus most desirable, yet the size of the network and the complexity of the controller makes this a challenging undertaking. In this paper we propose MOCS, a highly expressive, optimised SDN model that allows capturing subtle real-world bugs, in a reasonable amount of time. This is achieved by (1) analysing the model for possible partial order reductions, (2) statically pre-computing packet equivalence classes and (3) indexing packets and rules that exist in the model. We demonstrate its superiority compared to the state of the art in terms of expressivity, by providing examples of realistic bugs that a prototype implementation of MOCS in UPPAAL caught, and performance/scalability, by running examples on various sizes of network topologies, highlighting the importance of our abstractions and optimisations

Implicitization of curves and (hyper)surfaces using predicted support

We reduce implicitization of rational planar parametric curves and (hyper)surfaces to linear algebra, by interpolating the coefficients of the implicit equation. For predicting the implicit support, we focus on methods that exploit input and output structure in the sense of sparse (or toric) elimination theory, namely by computing the Newton polytope of the implicit polynomial, via sparse resultant theory. Our algorithm works even in the presence of base points but, in this case, the implicit equation shall be obtained as a factor of the produced polynomial. We implement our methods on Maple, and some on Matlab as well, and study their numerical stability and efficiency on several classes of curves and surfaces. We apply our approach to approximate implicitization, and quantify the accuracy of the approximate output, which turns out to be satisfactory on all tested examples; we also relate our measures to Hausdorff distance. In building a square or rectangular matrix, an important issue is (over)sampling the given curve or surface: we conclude that unitary complexes offer the best tradeoff between speed and accuracy when numerical methods are employed, namely SVD, whereas for exact kernel computation random integers is the method of choice. We compare our prototype to existing software and find that it is rather competitive

Non-perturbative features of driven scattering systems

We investigate the scattering properties of one-dimensional, periodically and non-periodically forced oscillators. The pattern of singularities of the scattering function, in the periodic case, shows a characteristic hierarchical structure where the number Nc of zeros of the solutions plays the role of an order parameter marking the level of the observed self-similar structure. The behavior is understood both in terms of the return map and of the intersections pattern of the invariant manifolds of the outermost fixed points. In the non-periodic case the scattering function does not provide a complete development of the hierarchical structure. The singularities pattern of the outgoing energy as a function of the driver amplitude is connected to the arrangement of gaps in the fundamental regions. The survival probability distribution of temporarily bound orbits is shown to decay asymptotically as a power law. The "stickiness" of regular regions of phase space, given by KAM surfaces and remnant of KAM curves, is responsible for this observation

Higher Impurity AdS/CFT Correspondence in the Near-BMN Limit

The pp-wave/BMN limit of the AdS/CFT correspondence has exposed the Maldacena conjecture to a new regimen of direct tests. In one line of pursuit, finite-radius curvature corrections to the Penrose limit (which appear in inverse powers of the string angular momentum J) have been found to induce a complicated system of interaction perturbations to string theory on the pp-wave; these have been successfully matched to corresponding corrections to the BMN dimensions of N=4 super Yang-Mills (SYM) operators to two loops in the 't Hooft coupling lambda. This result is tempered by a well-established breakdown in the correspondence at three loops. Notwithstanding the third-order mismatch, we proceed with this line of investigation by subjecting the string and gauge theories to new and significantly more rigorous tests. Specifically, we extend our earlier results at O(1/J) in the curvature expansion to include string states and SYM operators with three worldsheet or R-charge impurities. In accordance with the two-impurity problem, we find a perfect and intricate agreement between both sides of the correspondence to two-loop order in lambda and, once again, the string and gauge theory predictions fail to agree at third order.Comment: 45 pages, LaTeX; notation and references correcte