Relevant bibliographies by topics / Guaranteed computations

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  2. Dissertations / Theses
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Academic literature on the topic 'Guaranteed computations'

Author: Grafiati
Published: 1 February 2025
Last updated: 13 July 2025

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Journal articles on the topic "Guaranteed computations"

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YANG, ZHONGHUA, CHENGZHENG SUN, YUAN MIAO, ABDUL SATTAR, and YANYAN YANG. "GUARANTEED MUTUALLY CONSISTENT CHECKPOINTING IN DISTRIBUTED COMPUTATIONS." International Journal of Foundations of Computer Science 11, no. 01 (2000): 153–66. http://dx.doi.org/10.1142/s0129054100000089.

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In this paper, we explore the isomorphism between vector time and causality to characterize consistency of a set of checkpoints in a distributed computing. A necessary and sufficient condition, to determine if a set of local checkpoints can form a consistent global checkpoint, is presented and proved using the isomorphic power of vector time and causality. To the best of our knowledge, this is the first attempt to use the isomorphism for this purpose. This condition leads to a simple and straightforward algorithm for a guaranteed mutually consistent global checkpointing. In our approach, a process can take a checkpoint whenever and wherever it wants while other related process may be asked to take an additional checkpoint for ensuring the mutual consistency. We also show how this condition and the resulting algorithm can be used to obtain a maximum and minimum global checkpoints, another important paradigm for distributed applications.
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YONG, XIE, and HSU WEN-JING. "ALIGNED MULTITHREADED COMPUTATIONS AND THEIR SCHEDULING WITH PERFORMANCE GUARANTEES." Parallel Processing Letters 13, no. 03 (2003): 353–64. http://dx.doi.org/10.1142/s0129626403001331.

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This paper considers the problem of scheduling dynamic parallel computations to achieve linear speedup without using significantly more space per processor than that required for a single processor execution. Earlier research in the Cilk project proposed the "strict" computational model, in which every dependency goes from a thread x only to one of x's ancestor threads, and guaranteed both linear speedup and linear expansion of space. However, Cilk threads are stateless, and the task graph that Cilk language expresses is series-parallel graph, which is a proper subset of arbitrary task graph. Moreover, Cilk does not support applications with pipelining. We propose the "aligned" multithreaded computational model, which extends the "strict" computational model in Cilk. In the aligned multithreaded computational model, dependencies can go from arbitrary thread x not only to x's ancestor threads, but also to x's younger brother threads, that are spawned by x's parent thread but after x. We use the same measures of time and space as those used in Cilk: T1 is the time required for executing the computation on 1 processor, T∞ is the time required by an infinite number of processors, and S1 is the space required to execute the computation on 1 processor. We show that for any aligned computation, there exists an execution schedule that achieves both efficient time and efficient space. Specifically, we show that for an execution of any aligned multithreaded computation on P processors, the time required is bounded by O(T1/P + T∞), and the space required can be loosely bounded by O(λ·S1P), where λ is the maximum number of younger brother threads that have the same parent thread and can be blocked during execution. If we assume that λ is a constant, and the space requirements for elder and younger brother threads are the same, then the space required would be bounded by O(S1P). Based on the aligned multithreaded computational model, we show that the aligned multithreaded computational model supports pipelined applications. Furthermore, we propose a multithreaded programming language and show that it can express arbitrary task graph.
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Evstigneev, Nikolay M., and Oleg I. Ryabkov. "Reduction in Degrees of Freedom for Large-Scale Nonlinear Systems in Computer-Assisted Proofs." Mathematics 11, no. 20 (2023): 4336. http://dx.doi.org/10.3390/math11204336.

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In many physical systems, it is important to know the exact trajectory of a solution. Relevant applications include celestial mechanics, fluid mechanics, robotics, etc. For cases where analytical methods cannot be applied, one can use computer-assisted proofs or rigorous computations. One can obtain a guaranteed bound for the solution trajectory in the phase space. The application of rigorous computations poses few problems for low-dimensional systems of ordinary differential equations (ODEs) but is a challenging problem for large-scale systems, for example, systems of ODEs obtained from the discretization of the PDEs. A large-scale system size for rigorous computations can be as small as about a hundred ODE equations because computational complexity for rigorous algorithms is much larger than that for simple computations. We are interested in the application of rigorous computations to the problem of proving the existence of a periodic orbit in the Kolmogorov problem for the Navier–Stokes equations. One of the key issues, among others, is the computation complexity, which increases rapidly with the growth of the problem dimension. In previous papers, we showed that 79 degrees of freedom are needed in order to achieve convergence of the rigorous algorithm only for the system of ordinary differential equations. Here, we wish to demonstrate the application of the proper orthogonal decomposition (POD) in order to approximate the attracting set of the system and reduce the dimension of the active degrees of freedom.
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Ainsworth, Mark, and Richard Rankin. "Guaranteed computable bounds on quantities of interest in finite element computations." International Journal for Numerical Methods in Engineering 89, no. 13 (2012): 1605–34. http://dx.doi.org/10.1002/nme.3276.

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Xie, Dawei, Haining Yang, Jing Qin, and Jixin Ma. "Privacy-Preserving and Publicly Verifiable Protocol for Outsourcing Polynomials Evaluation to a Malicious Cloud." International Journal of Digital Crime and Forensics 11, no. 4 (2019): 14–27. http://dx.doi.org/10.4018/ijdcf.2019100102.

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As cloud computing provides affordable and scalable computational resources, delegating heavy computing tasks to the cloud service providers is appealing to individuals and companies. Among different types of specific computations, the polynomial evaluation is an important one due to its wide usage in engineering and scientific fields. Cloud service providers may not be trusted, thus, the validity and the privacy of such computation should be guaranteed. In this article, the authors present a protocol for publicly verifiable delegations of high degree polynomials. Compared with the existing solutions, it ensures the privacy of outsourced functions and actual results. And the protocol satisfies the property of blind verifiability such that the results can be publicly verified without learning the value. The protocol also improves in efficiency.
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LÊ, DINH, and D. STOTT PARKER. "Using randomization to make recursive matrix algorithms practical." Journal of Functional Programming 9, no. 6 (1999): 605–24. http://dx.doi.org/10.1017/s0956796899003470.

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Recursive block decomposition algorithms (also known as quadtree algorithms when the blocks are all square) have been proposed to solve well-known problems such as matrix addition, multiplication, inversion, determinant computation, block LDU decomposition and Cholesky and QR factorization. Until now, such algorithms have been seen as impractical, since they require leading submatrices of the input matrix to be invertible (which is rarely guaranteed). We show how to randomize an input matrix to guarantee that submatrices meet these requirements, and to make recursive block decomposition methods practical on well-conditioned input matrices. The resulting algorithms are elegant, and we show the recursive programs can perform well for both dense and sparse matrices, although with randomization dense computations seem most practical. By ‘homogenizing’ the input, randomization provides a way to avoid degeneracy in numerical problems that permits simple recursive quadtree algorithms to solve these problems.
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Ghoniem, Nasr M. "Curved Parametric Segments for the Stress Field of 3-D Dislocation Loops." Journal of Engineering Materials and Technology 121, no. 2 (1999): 136–42. http://dx.doi.org/10.1115/1.2812358.

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Under applied mechanical forces, strong mutual interaction or other thermodynamic forces, dislocation shapes become highly curved. We present here a new method for accurate computations of self and mutual interactions between dislocation loops. In this method, dislocation loops of arbitrary shapes are segmented with appropriate parametric equations representing the dislocation line vector. Field equations of infinitesimal linear elasticity are developed on the basis of isotropic elastic Green’s tensor functions. The accuracy and computational speed of the method are illustrated by computing the stress field around a typical (110)-[111] slip loop in a BCC crystal. The method is shown to be highly accurate for close-range dislocation interactions without any loss of computational speed when compared to analytic evaluations of the stress field for short linear segments. Moreover, computations of self-forces and energies of curved segments are guaranteed to be accurate, because of the continuity of line curvature on the loop.
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Bertrand, Fleurianne, Marcel Moldenhauer, and Gerhard Starke. "A Posteriori Error Estimation for Planar Linear Elasticity by Stress Reconstruction." Computational Methods in Applied Mathematics 19, no. 3 (2019): 663–79. http://dx.doi.org/10.1515/cmam-2018-0004.

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AbstractThe nonconforming triangular piecewise quadratic finite element space by Fortin and Soulie can be used for the displacement approximation and its combination with discontinuous piecewise linear pressure elements is known to constitute a stable combination for incompressible linear elasticity computations. In this contribution, we extend the stress reconstruction procedure and resulting guaranteed a posteriori error estimator developed by Ainsworth, Allendes, Barrenechea and Rankin [2] and by Kim [18] to linear elasticity. In order to get a guaranteed reliability bound with respect to the energy norm involving only known constants, two modifications are carried out: (i) the stress reconstruction in next-to-lowest order Raviart–Thomas spaces is modified in such a way that its anti-symmetric part vanishes in average on each element; (ii) the auxiliary conforming approximation is constructed under the constraint that its divergence coincides with the one for the nonconforming approximation. An important aspect of our construction is that all results hold uniformly in the incompressible limit. Global efficiency is also shown and the effectiveness is illustrated by adaptive computations involving different Lamé parameters including the incompressible limit case.
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Lindeberg, Tony. "Provably Scale-Covariant Continuous Hierarchical Networks Based on Scale-Normalized Differential Expressions Coupled in Cascade." Journal of Mathematical Imaging and Vision 62, no. 1 (2019): 120–48. http://dx.doi.org/10.1007/s10851-019-00915-x.

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Abstract This article presents a theory for constructing hierarchical networks in such a way that the networks are guaranteed to be provably scale covariant. We first present a general sufficiency argument for obtaining scale covariance, which holds for a wide class of networks defined from linear and nonlinear differential expressions expressed in terms of scale-normalized scale-space derivatives. Then, we present a more detailed development of one example of such a network constructed from a combination of mathematically derived models of receptive fields and biologically inspired computations. Based on a functional model of complex cells in terms of an oriented quasi quadrature combination of first- and second-order directional Gaussian derivatives, we couple such primitive computations in cascade over combinatorial expansions over image orientations. Scale-space properties of the computational primitives are analysed, and we give explicit proofs of how the resulting representation allows for scale and rotation covariance. A prototype application to texture analysis is developed, and it is demonstrated that a simplified mean-reduced representation of the resulting QuasiQuadNet leads to promising experimental results on three texture datasets.
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Likhoded, N. A., and M. A. Paliashchuk. "Tiled parallel 2D computational processes." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 54, no. 4 (2019): 417–26. http://dx.doi.org/10.29235/1561-2430-2018-54-4-417-426.

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The algorithm implemented on a parallel computer with distributed memory has, as a rule, a tiled structure: a set of operations is divided into subsets, called tiles. One of the modern approaches to obtaining tiled versions of algorithms is a tiling transformation based on information sections of the iteration space, resulting in macro-operations (tiles). The operations of one tile are performed atomically, as one unit of calculation, and the data exchange is done by arrays. The method of construction of tiled computational processes logically organized as a two-dimensional structure for algorithms given by multidimensional loops is stated. Compared to one-dimensional structures, the use of two-dimensional structures is possible in a smaller number of cases, but it can have advantages when implementing algorithms on parallel computers with distributed memory. Among the possible advantages are the reduction of the volume of communication operations, the reduction of acceleration and deceleration of computations, potentially a greater number of computation processes and the organization of data exchange operations only within the rows or columns of processes. The results are a generalization of some aspects of the method of construction of parallel computational processes organized in a one-dimensional structure to the case of a two-dimensional structure. It is shown that under certain restrictions on the structure and length of loops, it is sufficient to perform tiling on three coordinates of a multidimensional iteration space. In the earlier theoretical studies, the parallelism of tiled computations was guaranteed in the presence of information sections in all coordinates of the iteration space, and for a simpler case of a one-dimensional structure, in two coordinates.
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Dissertations / Theses on the topic "Guaranteed computations"

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Kanno, Masaaki. "Guaranteed accuracy computations in systems and control." Thesis, University of Cambridge, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.615686.

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Merdon, Christian. "Aspects of guaranteed error control in computations for partial differential equations." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2013. http://dx.doi.org/10.18452/16818.

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Diese Arbeit behandelt garantierte Fehlerkontrolle für elliptische partielle Differentialgleichungen anhand des Poisson-Modellproblems, des Stokes-Problems und des Hindernisproblems. Hierzu werden garantierte obere Schranken für den Energiefehler zwischen exakter Lösung und diskreten Finite-Elemente-Approximationen erster Ordnung entwickelt. Ein verallgemeinerter Ansatz drückt den Energiefehler durch Dualnormen eines oder mehrerer Residuen aus. Hinzu kommen berechenbare Zusatzterme, wie Oszillationen der gegebenen Daten, mit expliziten Konstanten. Für die Abschätzung der Dualnormen der Residuen existieren viele verschiedene Techniken. Diese Arbeit beschäftigt sich vorrangig mit Equilibrierungsschätzern, basierend auf Raviart-Thomas-Elementen, welche effiziente garantierte obere Schranken ermöglichen. Diese Schätzer werden mit einem Postprocessing-Verfahren kombiniert, das deren Effizienz mit geringem zusätzlichen Rechenaufwand deutlich verbessert. Nichtkonforme Finite-Elemente-Methoden erzeugen zusätzlich ein Inkonsistenzresiduum, dessen Dualnorm mit Hilfe diverser konformer Approximationen abgeschätzt wird. Ein Nebenaspekt der Arbeit betrifft den expliziten residuen-basierten Fehlerschätzer, der für gewöhnlich optimale und leicht zu berechnende Verfeinerungsindikatoren für das adaptive Netzdesign liefert, aber nur schlechte garantierte obere Schranken. Eine neue Variante, die auf den equilibrierten Flüssen des Luce-Wohlmuth-Fehlerschätzers basiert, führt zu stark verbesserten Zuverlässigkeitskonstanten. Eine Vielzahl numerischer Experimente vergleicht alle implementierten Fehlerschätzer und zeigt, dass effiziente und garantierte Fehlerkontrolle in allen vorliegenden Modellproblemen möglich ist. Insbesondere zeigt ein Modellproblem, wie die Fehlerschätzer erweitert werden können, um auch auf Gebieten mit gekrümmten Rändern garantierte obere Schranken zu liefern.<br>This thesis studies guaranteed error control for elliptic partial differential equations on the basis of the Poisson model problem, the Stokes equations and the obstacle problem. The error control derives guaranteed upper bounds for the energy error between the exact solution and different finite element discretisations, namely conforming and nonconforming first-order approximations. The unified approach expresses the energy error by dual norms of one or more residuals plus computable extra terms, such as oscillations of the given data, with explicit constants. There exist various techniques for the estimation of the dual norms of such residuals. This thesis focuses on equilibration error estimators based on Raviart-Thomas finite elements, which permit efficient guaranteed upper bounds. The proposed postprocessing in this thesis considerably increases their efficiency at almost no additional computational costs. Nonconforming finite element methods also give rise to a nonconsistency residual that permits alternative treatment by conforming interpolations. A side aspect concerns the explicit residual-based error estimator that usually yields cheap and optimal refinement indicators for adaptive mesh refinement but not very sharp guaranteed upper bounds. A novel variant of the residual-based error estimator, based on the Luce-Wohlmuth equilibration design, leads to highly improved reliability constants. A large number of numerical experiments compares all implemented error estimators and provides evidence that efficient and guaranteed error control in the energy norm is indeed possible in all model problems under consideration. Particularly, one model problem demonstrates how to extend the error estimators for guaranteed error control on domains with curved boundary.
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Merdon, Christian [Verfasser], Carsten Akademischer Betreuer] Carstensen, Andreas [Akademischer Betreuer] Schröder, and Stefan [Akademischer Betreuer] [Funken. "Aspects of guaranteed error control in computations for partial differential equations / Christian Merdon. Gutachter: Carsten Carstensen ; Andreas Schröder ; Stefan Funken." Berlin : Humboldt Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2013. http://d-nb.info/1042247005/34.

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Louédec, Morgan. "Guaranteed ellipsoidal numerical method for the stability analysis of the formation control of a group of underwater robots." Electronic Thesis or Diss., Brest, École nationale supérieure de techniques avancées Bretagne, 2024. http://www.theses.fr/2024ENTA0007.

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Pour développer les activités marines humaines, des groupes de robots sous-marins peuvent automatiser certaines tâches. Ces robots étant difficiles à localiser en raison de contraintes sous-marines, ils doivent se déplacer en formation pour être fiables. Bien que plusieurs contrôleurs théoriques aient été proposés pour faire face à ces contraintes, ils doivent encore s’adapter à des contraintes plus complexes et être testés sur des systèmes réels. Comme pour tout système autonome, la stabilité de la formation doit être vérifiée par une preuve mathématique. Cependant, la complexité de ces systèmes non linéaires rend la méthode de Lyapunov conventionnelle difficile à utiliser. Ainsi, l’objectif principal de cette thèse est de développer des méthodes numériques garanties, basées sur l’arithmétique des intervalles, qui peuvent assister la preuve de stabilité. Basée sur la propagation garantie ellipsoïdale, une première méthode est conçue pour les systèmes à temps discret afin de calculer un domaine d’attraction ellipsoïdal. Cette méthode est ensuite étendue aux systèmes à temps continu, puis aux systèmes hybrides synchrones, qui sont des modélisations plus réalistes. En outre, la propagation ellipsoïdale est étendue pour prendre en compte les applications singulières et les ellipsoïdes dégénérées. Enfin, des test de formation en situation réelle viennent illustrer la stabilité<br>In the development of human marine activity, groups of underwater robots can automate certain tasks. Since these robots are difficult to localise because of the underwater constrains, they must move in formation to be reliable. While various theoretical controllers have been proposed to challenge these constrains, they still need to consider more complex constrains and to be tested on real systems. As for every autonomous system, the stability of the formation must be verified by a mathematical proof. However, the complexity of these nonlinear systems makes conventional Lyapunov method difficult to use. Thus, this thesis’ main objective is to develop guaranteed numerical methods, based on interval arithmetic, that can assist the stability proof. Based on ellipsoidal guaranteed propagation, a first method is designed for discrete time systems to compute an ellipsoidal domain of attraction. This method is then extended to continuous-time systems and then to synchronous hybrid systems which are more realistic modellings. In addition, the ellipsoidal propagation is extended to consider singular mappings and degenerate ellipsoids. Finally, some real world underwater formation control was achieved to illustrate the stability
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Kratz, Gutstav. "Risk Modelling in Payment Guarantees." Thesis, KTH, Matematisk statistik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-229418.

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The Swedish Export Credit Agency (EKN) issues payment guarantees to Swedish companies who face the risk of non-payments in export transactions. Commitments are typically correlated, as defaults of companies are driven by other factors than factors specific to that company, such as the economic cycle or the regional conditions. In deciding upon how much capital to be reserved to remain solvent even in an unlikely scenario, this has to be accounted for in order to not underestimate financial risks.By studying models for credit risk and the research available in the area, the popular CreditRisk+ has been chosen as a suitable model for EKN to use in risk assessments. The model together with a few customizations are described in detail and tested on data from EKN.<br>Exportkreditnämnden (EKN) utfärdar betalningsgarantier till svenska exportörer som riskerar inställda betalningar. Fallissemang hos olika motparter är typiskt korrelerade. Vid bedömning av risken i portföljen av garantier måste detta tas i beaktning, för att inte underskatta risken väsentligt. Genom att studera befintliga kreditriskmodeller och tillgänglig forskning inom området har en modell föreslagits som kan användas i EKN:s riskbedömningar. Modellen beskrivs i detalj och testas på data från EKN.
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Lu, Yu. "Statistical and Computational Guarantees for Learning Latent Variable Models." Thesis, Yale University, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10783452.

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<p> Latent variable models are widely used to capture the underlying structures of the data, for example, Gaussian mixture models for speech recognition, stochastic block models for community detection and topic models for information retrieval. While alternative minimization based algorithms such as EM algorithm and Lloyd's algorithm performs well in practice, there has been little theoretical advancement in explaining the effectiveness of these algorithms. In this thesis, we investigate the performance of Lloyd's algorithm and EM algorithm on clustering two-mixture of Gaussians. With an initializer slightly better than random guess, we are able to show the linear converge of Lloyd's and EM iterations to the statistical optimal estimator. These results shed light on the global convergence of more general non-convex optimizations.</p><p> We generalized the results to arbitrary number of sub-Gaussian mixtures. Motivated by the Lloyd's algorithm, we propose new algorithms for other latent variable models including sparse gaussian mixture model, stochastic block model. biclustering model and Dawid-Skene model. The proposed algorithms are computationally efficient and shown to be rate-optimal under mild signal-to-noise ratio conditions. The highlight of our theoretical analysis is to develop new proof techniques to handle the dependency between iterations, which can be applied to other iterative algorithms with explicit iteration formulas. </p><p>
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Kaynama, Shahab. "Scalable techniques for the computation of viable and reachable sets : safety guarantees for high-dimensional linear time-invariant systems." Thesis, University of British Columbia, 2012. http://hdl.handle.net/2429/42856.

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Reachability analysis and viability theory are key in providing guarantees of safety and proving the existence of safety-preserving controllers for constrained dynamical systems. The minimal reachable tube and (by duality) the viability kernel are the only constructs that can be used for this purpose. Unfortunately, current numerical schemes that compute these constructs suffer from a complexity that is exponential in the dimension of the state, rendering them impractical for systems of dimension greater than three or four. In this thesis we propose two separate approaches that improve the scalability of the computation of the minimal reachable tube and the viability kernel for high-dimensional systems. The first approach is based on structure decomposition and aims to facilitate the use of computationally intensive yet versatile and powerful tools for higher-dimensional linear time-invariant (LTI) systems. Within the structure decomposition framework we present two techniques – Schur-based and Riccati-based decompositions – that impose an appropriate structure on the system which is then exploited for the computation of our desired constructs in lower-dimensional subspaces. The second approach is based on set-theoretic methods and draws a new connection between the viability kernel and maximal reachable sets. Existing tools that compute the maximal reachable sets are efficient and scalable with polynomial complexity in time and space. As such, these scalable techniques can now be used to compute our desired constructs and therefore provide guarantees of safety for high-dimensional systems. Based on this new connection between the viability kernel and maximal reachable sets we propose a scalable algorithm using ellipsoidal techniques for reachability. We show that this algorithm can efficiently compute a conservative under-approximation of the viability kernel (or the discriminating kernel when uncertainties are present) for LTI systems. We then propose a permissive state-feedback control strategy that is capable of preserving safety despite bounded input authority and possibly unknown disturbances or model uncertainties for high-dimensional systems. We demonstrate the results of both of our approaches on a number of practical examples including a problem of safety in control of anesthesia and a problem of aerodynamic flight envelope protection.
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Herhut, S. "Auxiliary computations : a framework for a step-wise, non-disruptive introduction of static guarantees to untyped programs using partial evaluation techniques." Thesis, University of Hertfordshire, 2010. http://hdl.handle.net/2299/4722.

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Type inference can be considered a form of partial evaluation that only evaluates a program with respect to its type annotations. Building on this key observation, this dissertation presents a uniform framework for expressing computation, its dynamic properties and corresponding static type information. By using a unified approach, the static phase divide between values and types is lifted. Instead, computations and properties can be freely assigned to the static or dynamic phase of computation. Even more, moving a property from one world to the other does not require any program modifications. This thesis builds a bridge between two worlds: That of statically typed languages and the dynamically typed world. The former is wanted for the offered static guarantees and detection of a range of defects. With the increasing power of type systems available, the kinds of errors that can be statically detected is growing, nearing the goal of proving overall program correctness from the program’s source code alone. However, such power does come for a price: Type systems are becoming more complex, restrictive and invasive, to the point where specifying type annotations becomes as complex as specifying the algorithm itself. Untyped languages, in contrast, may provide less static safety but they have simpler semantics and offer a higher flexibility. They allow programmers to express their ideas without worrying about provable correctness. Not surprisingly, untyped languages have a strong following when it comes to prototyping and rapid application development. Using the framework presented in this thesis, the programmer can have both: Prototyping applications using a dynamically typed approach and gradual refinement of prototypes into programs with static guarantees. Technically, this flexibility is achieved with the novel concept of auxiliary computations. Auxiliary computation are additional streams of computation. They model, next to the data’s computation, the computation of property of data. These streams thereby may depend on the actual data that is computed, as well as on further auxiliary computations. This expressiveness brings auxiliary computations into the domain of dependent types. Partial evaluation of auxiliary computations is used to infer static knowledge from auxiliary computations. Due to the interdependencies between auxiliary computations, evaluating only those parts of a program that contribute to a property is non trivial. A further contribution of this work is the use of demands on computations to narrow the extent of partial evaluation to a single property. An algorithm for demand inference is presented and the correctness of the inferred demands is shown.
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Feng, Lu. "On learning assumptions for compositional verification of probabilistic systems." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:12502ba2-478f-429a-a250-6590c43a8e8a.

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Probabilistic model checking is a powerful formal verification method that can ensure the correctness of real-life systems that exhibit stochastic behaviour. The work presented in this thesis aims to solve the scalability challenge of probabilistic model checking, by developing, for the first time, fully-automated compositional verification techniques for probabilistic systems. The contributions are novel approaches for automatically learning probabilistic assumptions for three different compositional verification frameworks. The first framework considers systems that are modelled as Segala probabilistic automata, with assumptions captured by probabilistic safety properties. A fully-automated approach is developed to learn assumptions for various assume-guarantee rules, including an asymmetric rule Asym for two-component systems, an asymmetric rule Asym-N for n-component systems, and a circular rule Circ. This approach uses the L* and NL* algorithms for automata learning. The second framework considers systems where the components are modelled as probabilistic I/O systems (PIOSs), with assumptions represented by Rabin probabilistic automata (RPAs). A new (complete) assume-guarantee rule Asym-Pios is proposed for this framework. In order to develop a fully-automated approach for learning assumptions and performing compositional verification based on the rule Asym-Pios, a (semi-)algorithm to check language inclusion of RPAs and an L*-style learning method for RPAs are also proposed. The third framework considers the compositional verification of discrete-time Markov chains (DTMCs) encoded in Boolean formulae, with assumptions represented as Interval DTMCs (IDTMCs). A new parallel operator for composing an IDTMC and a DTMC is defined, and a new (complete) assume-guarantee rule Asym-Idtmc that uses this operator is proposed. A fully-automated approach is formulated to learn assumptions for rule Asym-Idtmc, using the CDNF learning algorithm and a new symbolic reachability analysis algorithm for IDTMCs. All approaches proposed in this thesis have been implemented as prototype tools and applied to a range of benchmark case studies. Experimental results show that these approaches are helpful for automating the compositional verification of probabilistic systems through learning small assumptions, but may suffer from high computational complexity or even undecidability. The techniques developed in this thesis can assist in developing scalable verification frameworks for probabilistic models.
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(11196552), Kevin Segundo Bello Medina. "STRUCTURED PREDICTION: STATISTICAL AND COMPUTATIONAL GUARANTEES IN LEARNING AND INFERENCE." Thesis, 2021.

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<div>Structured prediction consists of receiving a structured input and producing a combinatorial structure such as trees, clusters, networks, sequences, permutations, among others. From the computational viewpoint, structured prediction is in general considered <i>intractable</i> because of the size of the output space being exponential in the input size. For instance, in image segmentation tasks, the number of admissible segments is exponential in the number of pixels. A second factor is the combination of the input dimensionality along with the amount of data under availability. In structured prediction it is common to have the input live in a high-dimensional space, which involves to jointly reason about thousands or millions of variables, and at the same time contend with limited amount of data. Thus, learning and inference methods with strong computational and statistical guarantees are desired. The focus of our research is then to propose <i>principled methods</i> for structured prediction that are both polynomial time, i.e., <i>computationally efficient</i>, and require a polynomial number of data samples, i.e., <i>statistically efficient</i>.</div><div><br></div><div>The main contributions of this thesis are as follows:</div><div><br></div><div>(i) We develop an efficient and principled learning method of latent variable models for structured prediction under Gaussian perturbations. We derive a Rademacher-based generalization bound and argue that the use of non-convex formulations in learning latent-variable models leads to tighter bounds of the Gibbs decoder distortion.</div><div><br></div><div>(ii) We study the fundamental limits of structured prediction, i.e., we characterize the necessary sample complexity for learning factor graph models in the context of structured prediction. In particular, we show that the finiteness of our novel MaxPair-dimension is necessary for learning. Lastly, we show a connection between the MaxPair-dimension and the VC-dimension---which allows for using existing results on VC-dimension to calculate the MaxPair-dimension.</div><div><br></div><div>(iii) We analyze a generative model based on connected graphs, and find the structural conditions of the graph that allow for the exact recovery of the node labels. In particular, we show that exact recovery is realizable in polynomial time for a large class of graphs. Our analysis is based on convex relaxations, where we thoroughly analyze a semidefinite program and a degree-4 sum-of-squares program. Finally, we extend this model to consider linear constraints (e.g., fairness), and formally explain the effect of the added constraints on the probability of exact recovery.</div><div><br></div>
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Books on the topic "Guaranteed computations"

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Liu, Xuefeng. Guaranteed Computational Methods for Self-Adjoint Differential Eigenvalue Problems. Springer Nature Singapore, 2024. http://dx.doi.org/10.1007/978-981-97-3577-8.

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Guaranteed Computational Methods for Self-Adjoint Differential Eigenvalue Problems. Springer, 2024.

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Miranker, Willard L., Edgar W. Kaucher, and Werner Rheinboldt. Self-Validating Numerics for Function Space Problems: Computation with Guarantees for Differential and Integral Equations. Elsevier Science & Technology Books, 2014.

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Succi, Sauro. Lattice Boltzmann Models for Microflows. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0029.

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The Lattice Boltzmann method was originally devised as a computational alternative for the simulation of macroscopic flows, as described by the Navier–Stokes equations of continuum mechanics. In many respects, this still is the main place where it belongs today. Yet, in the past decade, LB has made proof of a largely unanticipated versatility across a broad spectrum of scales, from fully developed turbulence, to microfluidics, all the way down to nanoscale flows. Even though no systematic analogue of the Chapman–Enskog asymptotics is available in this beyond-hydro region (no guarantee), the fact remains that, with due extensions of the basic scheme, the LB has proven capable of providing several valuable insights into the physics of flows at micro- and nano-scales. This does not mean that LBE can solve the actual Boltzmann equation or replace Molecular Dynamics, but simply that it can provide useful insights into some flow problems which cannot be described within the realm of the Navier–Stokes equations of continuum mechanics. This Chapter provides a cursory view of this fast-growing front of modern LB research.
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Book chapters on the topic "Guaranteed computations"

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Godunov, S. K., A. G. Antonov, O. P. Kiriljuk, and V. I. Kostin. "Peculiarities of Computer Computations." In Guaranteed Accuracy in Numerical Linear Algebra. Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-1952-8_5.

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Schauer, U., and R. A. Toupin. "Solving large sparse linear systems with guaranteed accuracy." In Accurate Scientific Computations. Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/3-540-16798-6_8.

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Yang, Zhonghua, Chengzheng Sun, Abdul Sattar, and Yanyan Yang. "Guaranteed Mutually Consistent Checkpointing in Distributed Computations." In Advances in Computing Science ASIAN 98. Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/3-540-49366-2_13.

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Liu, Xuefeng. "Guaranteed Eigenfunction Computation." In Guaranteed Computational Methods for Self-Adjoint Differential Eigenvalue Problems. Springer Nature Singapore, 2024. http://dx.doi.org/10.1007/978-981-97-3577-8_6.

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Xu, Runqing, Liming Li, and Bohua Zhan. "Verified Interactive Computation of Definite Integrals." In Automated Deduction – CADE 28. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-79876-5_28.

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AbstractSymbolic computation is involved in many areas of mathematics, as well as in analysis of physical systems in science and engineering. Computer algebra systems present an easy-to-use interface for performing these calculations, but do not provide strong guarantees of correctness. In contrast, interactive theorem proving provides much stronger guarantees of correctness, but requires more time and expertise. In this paper, we propose a general framework for combining these two methods, and demonstrate it using computation of definite integrals. It allows the user to carry out step-by-step computations in a familiar user interface, while also verifying the computation by translating it to proofs in higher-order logic. The system consists of an intermediate language for recording computations, proof automation for simplification and inequality checking, and heuristic integration methods. A prototype is implemented in Python based on HolPy, and tested on a large collection of examples at the undergraduate level.
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Kieffer, Michel, Isabelle Braems, Éric Walter, and Luc Jaulin. "Guaranteed Set Computation with Subpavings." In Scientific Computing, Validated Numerics, Interval Methods. Springer US, 2001. http://dx.doi.org/10.1007/978-1-4757-6484-0_14.

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Jaulin, Luc, Michel Kieffer, Olivier Didrit, and Éric Walter. "Guaranteed Computation with Floating-point Numbers." In Applied Interval Analysis. Springer London, 2001. http://dx.doi.org/10.1007/978-1-4471-0249-6_10.

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Mali, Olli, Pekka Neittaanmäki, and Sergey Repin. "Guaranteed Error Bounds I." In Computational Methods in Applied Sciences. Springer Netherlands, 2014. http://dx.doi.org/10.1007/978-94-007-7581-7_3.

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Mali, Olli, Pekka Neittaanmäki, and Sergey Repin. "Guaranteed Error Bounds II." In Computational Methods in Applied Sciences. Springer Netherlands, 2014. http://dx.doi.org/10.1007/978-94-007-7581-7_4.

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Flórez, Jorge, Mateu Sbert, Miguel A. Sainz, and Josep Vehí. "Guaranteed Adaptive Antialiasing Using Interval Arithmetic." In Computational Science – ICCS 2007. Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-72586-2_24.

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Conference papers on the topic "Guaranteed computations"

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Jimenez-Garcia, Antonio, and George Barakos. "Implementation of High-Order Methods in the HMB CFD Solver." In Vertical Flight Society 73rd Annual Forum & Technology Display. The Vertical Flight Society, 2017. http://dx.doi.org/10.4050/f-0073-2017-12011.

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This work presents the development and implementation of an efficient, compact high-order finite-volume scheme in the HMB CFD solver. This formulation is based on the variable extrapolation MUSCL-scheme, where high-order spatial accuracy (up to 4th-order) is achieved using high-order correction terms through a successive differentiation. The scheme has also been modified to cope with physical and multiblock mesh interfaces, so stability, conservativeness, and high-order accuracy are guaranteed. A wide variety of results for the underlying method are presented, including two-and three-dimensional test cases. The convection of an isentropic vortex, and the aerodynamic interaction between a vortex and a NACA-0012 aerofoil (blade vortex interaction problem BVI) are first studied, demonstrating the high level of accuracy of the new formulation. Theoretical and numerical analyses of the truncation error are also included. The three-dimensional steady flows around the 7AD, S-76, and XV-15 blades are also computed. Results with the proposed scheme, showed better wake and higher resolution of the vortical structures compared with the standard MUSCL solution, even though a coarse mesh was employed. The method was also demonstrated to three-dimensional unsteady flows using overset and moving grid computations for the UH-60A rotor in forward flight. The effect that the present method adds a CPU overhead of 40% in performing multi-dimensional problems encourages its use for routine computations.
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Aras, Chinmay M., Ashfaq Iftakher, and M. M. Faruque Hasan. "Guaranteed Error-bounded Surrogate Framework for Solving Process Simulation Problems." In Foundations of Computer-Aided Process Design. PSE Press, 2024. http://dx.doi.org/10.69997/sct.182073.

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Process simulation problems often involve systems of nonlinear and nonconvex equations and may run into convergence issues due to the existence of recycle loops within such models. To that end, surrogate models have gained significant attention as an alternative to high-fidelity models as they significantly reduce the computational burden. However, these models do not always provide a guarantee on the prediction accuracy over the domain of interest. To address this issue, we strike a balance between computational complexity by developing a data-driven branch and prune-based framework that progressively leads to a guaranteed solution to the original system of equations. Specifically, we utilize interval arithmetic techniques to exploit Hessian information about the model of interest. Along with checking whether a solution can exist in the domain under consideration, we generate error-bounded convex hull surrogates using the sampled data and Hessian information. When integrated in a branch and prune framework, the branching leads to the domain under consideration becoming smaller, thereby reducing the quantified prediction error of the surrogate, ultimately yielding a solution to the system of equations. In this manner, we overcome the convergence issues that are faced by many simulation packages. We demonstrate the applicability of our framework through several case studies. We first utilize a set of test problems from literature. For each of these test systems, we can find a valid solution. We then demonstrate the efficacy of our framework on real-world process simulation problems.
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Kanno, M., and M. C. Smith. "Guaranteed accuracy computations in systems and control." In 2003 European Control Conference (ECC). IEEE, 2003. http://dx.doi.org/10.23919/ecc.2003.7084967.

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Bajard, Jean-Claude, Philippe Langlois, Dominique Michelucci, Géraldine Morin, and Nathalie Revol. "Floating-point geometry: toward guaranteed geometric computations with approximate arithmetics." In Optical Engineering + Applications, edited by Franklin T. Luk. SPIE, 2008. http://dx.doi.org/10.1117/12.796597.

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Abdeltawab, Hussein. "Optimal Stochastic Dispatch of Combined Heat Power System with Guaranteed Heat Trading." In 2022 10th International Japan-Africa Conference on Electronics, Communications, and Computations (JAC-ECC). IEEE, 2022. http://dx.doi.org/10.1109/jac-ecc56395.2022.10043939.

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Dudaško, Ján, and Bernhard Semlitsch. "On the Numerical Efficacy Evaluation of Industrial Droplet Separators." In ASME 2024 Power Conference. American Society of Mechanical Engineers, 2024. http://dx.doi.org/10.1115/power2024-138858.

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Abstract Droplet separators are essential components of the chemical process chain. If malfunctioning, the remaining droplets can damage the downstream elements. Thus, reliable functioning is critical and has to be guaranteed for all operating conditions. Computational fluid dynamic computations are commonly employed to analyse the turbulent flow in droplet separators and predict their efficiency. The two-phase flow is modelled using the k-omega SST turbulence model, while the trajectories of fluid particle distributions are computed to quantify the droplet separator efficiency. Fine wall resolutions are required to accurately predict the establishing water film on the solid walls. The industrial size of droplet separators can reach internal length scales over several meters, which is challenging due to the scale differences in the modelling strategies. We investigate the efficiency of industrial droplet separators by numerical simulations and show the application of the computational methodology based on examples. Over 36 million polyhedral mesh cells with wall-layer refinement are employed to obtain the best results. The flow field is analysed to identify the potential for improvement in terms of pressure drop and separation efficiency.
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Law, Mark, Krysia Broda, and Alessandra Russo. "Search Space Expansion for Efficient Incremental Inductive Logic Programming from Streamed Data." In Thirty-First International Joint Conference on Artificial Intelligence {IJCAI-22}. International Joint Conferences on Artificial Intelligence Organization, 2022. http://dx.doi.org/10.24963/ijcai.2022/374.

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In the past decade, several systems for learning Answer Set Programs (ASP) have been proposed, including the recent FastLAS system. Compared to other state-of-the-art approaches to learning ASP, FastLAS is more scalable, as rather than computing the hypothesis space in full, it computes a much smaller subset relative to a given set of examples that is nonetheless guaranteed to contain an optimal solution to the task (called an OPT-sufficient subset). On the other hand, like many other Inductive Logic Programming (ILP) systems, FastLAS is designed to be run on a fixed learning task meaning that if new examples are discovered after learning, the whole process must be run again. In many real applications, data arrives in a stream. Rerunning an ILP system from scratch each time new examples arrive is inefficient. In this paper we address this problem by presenting IncrementalLAS, a system that uses a new technique, called hypothesis space expansion, to enable a FastLAS-like OPT-sufficient subset to be expanded each time new examples are discovered. We prove that this preserves FastLAS's guarantee of finding an optimal solution to the full task (including the new examples), while removing the need to repeat previous computations. Through our evaluation, we demonstrate that running IncrementalLAS on tasks updated with sequences of new examples is significantly faster than re-running FastLAS from scratch on each updated task.
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Arab, Aliasghar, Jingang Yi, Mohammad Mahdi Fateh, and Soroush Arabshahi. "Robust Control of a Low-Cost Mobile Robot Using a Neural Network Uncertainty Compensator." In ASME 2014 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/dscc2014-6190.

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This paper presents a robust control design for a low-cost mobile robot under modeling uncertainties and external disturbances. We use a radial basis function neural network (RBFNN) to estimate and compensate for the model uncertainties and external disturbances. The proposed control design is model-free with guaranteed stability and good path-following performance. The RBFNN weight regulation and adaptive gains are designed based on the Lypanov method. Simulation and experimental results illustrate the design and demonstrate the strength of the proposed control applied to a nonholonomic wheeled mobile robot driven by low-cost permanent magnet dc motors without shaft encoders. The comparison results between proposed control and feedback linearization control confirm the effective role of the compensator in terms of precision, simplicity of design and computations.
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Nicoud, Didier, Catherine Le Bloa, and Olivier-Pierre Jacquotte. "A Finite Element Inverse Method for the Design of Turbomachinery Blades." In ASME 1991 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/91-gt-080.

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We present a quasi-3D inverse method for the design of turbomachinery blades corresponding to a velocity distribution given arbitrarily. The theoretical aspect of the problem is first investigated, then the equations governing the quasi three-dimensional potential model are reviewed. The inverse method consists of solving the potential equation with Dirichlet boundary conditions on the profile, then modifying the profile iteratively until there is no mass flux through its surface. The convergence of the process is guaranteed by the preliminary theoretical study. The method is implemented using a finite element discretization, which relies on a mixed variational formulation involving two fields of unknowns: the velocity potential and the normal displacement of the profile. Several results are shown on subsonic and transonic compressor profiles. The modified profiles are then validated with direct calculations such as quasi three-dimensional Navier-Stokes computations. These results illustrate the behavior of the method, in particular its robustness and its effectiveness. The method was adapted to calculations on turbine blade profiles. Preliminary results are shown that illustrate an industrial use of the method on a subsonic profile.
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Qin, Yan, Yong Xiang, and Meilin Shi. "Core-stateless Fair Bandwidth Allocation for Guaranteed Services, Part I: End-to-end Precise Basic Bandwidth Guarantees." In Multiconference on "Computational Engineering in Systems Applications. IEEE, 2006. http://dx.doi.org/10.1109/cesa.2006.4281865.

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Reports on the topic "Guaranteed computations"

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Juvva, Kanaka. Coscheduling of Computation and Communication Resoures in Push-Pull Communications to Provide End-To-End QoS Guarantees. Defense Technical Information Center, 1999. http://dx.doi.org/10.21236/ada370066.

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