Jitka Snítilá · Digital Repository (National Repository of Grey Literature) · 2017
This thesis focuses on the lower bounds for generic algorithms for discrete logarithms problem and Diffie-Hellman's problems. This thesis introduces two diffrent models of Black-Box for that purpose. On these models thesis approxi- mates and compares success probability of generic algorithms for given problems including Maurer's reduction. This reduction solves discrete logarithms problem using a appropriate elliptic curve and a Diffie-Hellman's oracle. This thesis also researches generic algorithm for identifiaction schemes, that are based on discrete logarithms problem. 1
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Nachum Dershowitz, Evgenia Falkovich · Lecture notes in computer science · 2014
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Justin R Smith · 1993
Abstract We will consider how several different networks handle many common algorithms. In order to do this, we follow Preparata and Vuillemin in [125] in defining a pair of generic parallel algorithms that can be easily implemented on the common network-Naturally, some networks are better than others for developing parallel algorithms. Essentially, they have structural properties that make it easier to describe the data movement operations necessary for parallel computations. We will consider several such architectures in this chapter. In every case, physical computers have been con structed that implement the given architecture.
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Dietmar Kühl · Lecture notes in computer science · 2000
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Gregor Milicic, Sina Wetzel, Matthias Ludwig · Future Internet · 2020
Due to its links to computer science (CS), teaching computational thinking (CT) often involves the handling of algorithms in activities, such as their implementation or analysis. Although there already exists a wide variety of different tasks for various learning environments in the area of computer science, there is less material available for CT. In this article, we propose so-called Generic Tasks for algorithms inspired by common programming tasks from CS education. Generic Tasks can be seen as a family of tasks with a common underlying structure, format, and aim, and can serve as best-practice examples. They thus bring many advantages, such as facilitating the process of creating new content and supporting asynchronous teaching formats. The Generic Tasks that we propose were evaluated by 14 experts in the field of Science, Technology, Engineering, and Mathematics (STEM) education. Apart from a general estimation in regard to the meaningfulness of the proposed tasks, the experts also rated which and how strongly six core CT skills are addressed by the tasks. We conclude that, even though the experts consider the tasks to be meaningful, not all CT-related skills can be specifically addressed. It is thus important to define additional tasks for CT that are detached from algorithms and programming.
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Gaëtan Leurent · HAL (Le Centre pour la Communication Scientifique Directe) · 2015
International audience
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Vladimir Yakhnis, Jay A. Farrell, S. S. Shultz · IBM Systems Journal · 1994
We suggest a new approach to the derivation of programs from their specifications. The formal derivation and proof of programs as is practiced today is a very powerful tool for the development of high-quality software. However, its application by the software development community has been slowed by the amount of mathematical expertise needed to apply these formal methods to complex projects and by the lack of reuse within the framework of program derivation. To address these problems, we have developed an approach to formal derivation that employs the new concept of generic algorithms. A generic algorithm is one that has (1) a formal specification, (2) a proof that it satisfies this specification, and (3) generic identifiers representing types and operations. It may have embedded program specifications or pseudocode instructions describing the next steps in the stepwise refinement process. Using generic algorithms, most software developers need to know only how to pick and adapt them, rather than perform more technically challenging tasks such as finding loop invariants and deriving loop programs. The adaptation consists of replacing the generic identifiers by concrete types and operations. Since each generic algorithm can be used in the derivation of many different programs, this new methodology provides the developer with a form of reuse of program derivation techniques, correctness proofs, and formal specifications.
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Jacques-olivier Lachaud A · 2014
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Jeremy G. Siek, Lie‐Quan Lee, Andrew Lumsdaine · 2000
The Standard Template Library has established a solid foundation for the development of reusablealgorithms and data structures in C++. It has provided programmers with a way to think about designingreusable components (generic programming), and has demonstrated the programming techniques necessaryto build efficient implementations. However, there are many problem domains beyond those addressed bythe STL; consequently, there are many opportunities for applying generic programming. One particularlyimportant domain is that of graph algorithms and data structures. The graph abstraction is widely used tomodel structures and relationships in many fields. Graph algorithms are extremely important in such diverseapplication areas as design automation, transportation, optimization, and databases. Our own interest ingraph algorithms originates with our work on sparse matrix ordering algorithms for scientific computing.The domain of graph algorithms is ripe for the application of generic programming. There is a large existingbody of useful algorithms, yet the number of ways that people use to represent graphs in memory almostmatches the number of applications that use graphs. The ability to freely interchange graph algorithms withgraph representations would be an important contribution to the field, and this is what generic programminghas to offer.In January, 1999, we did a survey of existing graph libraries. Some of the libraries we looked at were LEDA(by Kurt Mehlhorn and Stefan Naeher, http:// www.mpi-sb.mpg.de/LEDA/leda.html), the Graph TemplateLibrary (GTL) (by Michael Forster, Andreas Pick, and Marcus Raitner, http://www.fmi.uni-passau.de/Graphlet/GTL/), Combinatorica (see
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Routing And Scheduling, Tore Grünert, Rheinisch-westfälische Technische et al. · 2003
The suggested framework has significant similarities with both these approaches, but also di#ers from them in several important aspects. It also uses the concept of resource variables and vectors as in [1], but allows for a more general update rule within routes and locations. Moreover, our focus is purely on heuristics, since the problem instances we consider cannot be solved to optimality with the algorithms available to us today. Using the concept of resource variables allows us to model the relevant constraints in a declarative way very similar to the constraint programming framework without the additional overhead 1 imposed by this approach. The result is that we will restrict ourselves to solving VRPSs where constraint propagation, which in our case corresponds to the determination of resource variables along routes and the locations visited by the routes, does not require any search. So far, we have not seen any practical problem where this assumption has limited the applicab
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Marcos Cordeiro d’Ornellas, R. van den Boomgaard · 1998
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Roberto Avanzi · 2005
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Elena Kartashova, Alexey Kartashov · Physica A Statistical Mechanics and its Applications · 2007
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Pierre Flener, Justin Pearson · 2008
Abstract. When a new (global) constraint is introduced in local search, measures for the penalty and variable conflicts of that constraint must be defined, and incremental algorithms for maintaining these measures must be implemented. These are complicated and time-consuming tasks, which clearly reduces the productivity of the local-search practitioner. We introduce a generic scheme that, from a description of a constraint in monadic existential second-order logic extended with counting, automatically gives penalty and variable-conflict measures for such a constraint, as well as incremental algorithms for maintaining these measures. We prove that our variable-conflict measure for a variable x is lower-bounded by the maximum penalty decrease that may be achieved by only changing the value of x, as well as upper bounded by the penalty measure. Without these properties, the local search performance may degrade. We also demonstrate the usefulness of the approach by replacing a built-in global constraint by a modelled version, while still obtaining competitive results in terms of runtime and robustness. This is especially attractive when a particular (global) constraint is not built in. 1
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Bland, I.M. · OpenGrey (Institut de l'Information Scientifique et Technique) · 2000
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Jorge Maturana, SAUBION, Frédéric · OpenGrey (Institut de l'Information Scientifique et Technique) · 2009
Les paramètres des Algorithmes Evolutionnaires (AEs) ont une forte influence sur leur capacité à produire de bons résultats. Ces paramètres définissent les aspects structuraux et comportementaux de l'AE, comme la définition des composants qui seront inclus (e.g., l'ensemble d'opérateurs à utiliser, le codage, le schéma de sélection) ou la façon dont ces composants seront employés (e.g., le taux d'application des opérateurs). La paramétrisation des AEs a et e longtemps un domaine de spécialistes, et même si de nombreuses études ont abordé le problème de la paramétrisation, il existe un déficit d'approches génériques qui puissent être appliquées à une grande variété d'AEs d'une manière simple. Cette thèse traite le problème de la conception d'un contrôleur générique, qui puisse être inclus dans n'importe quel AE avec un minimum d'efforts. Ceci est accompli en incorporant un composant d'apprentissage adaptatif, qui surveille l'état de la recherche et modifie les valeurs des paramètres. Le contrôleur se focalise sur les objectifs communs à tout EA, i.e., la maximisation de la diversité de la population et de la qualité des individus, afin de maintenir un équilibre convenable entre l'exploration et l'exploitation. Des nombreuses configurations des mécanismes d'apprentissage et d'ajustement ont et e essayées et analysées, en utilisant AEs différents qui résolvent des problèmes combinatoires connus. Les bons résultats obtenus suggèrent que notre objectif de construire un contrôleur générique et facile à utiliser constitue une approche encourageante.
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Holger Gast, Christoph Schwarzweller · 2015
Abstract. Algorithms in computer algebra lend themselves naturally to the software design method of generic programming in the sense of the C++ STL library [14]: They abstract over their concrete input domain in favour of the properties that the domain must have; when calling a generic algorithm, the instantiation domain must provide these proper-ties. We seek to design a language for generic programming; in particular, the compiler should be aware of the proof obligations associated with instantiation and should assist in proving them. Since properties will in general be formulated in a rich logic, we introduce symbolic adjectives as names for underlying formulae. The compiler then works on sets of adjectives as a representation for properties; relations between properties become declared implications between sets of adjectives. We present a concise prototypical language Saga (Signatures and Ad-jectives for Generic Algorithms) that embodies this design principle and demonstrate its applicability by example. 1
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Goos, Gerhard, Hartmanis, Juris, van Leeuwen, Jan · CERN Document Server (European Organization for Nuclear Research) · 2000
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Graham M. Megson, I.M. Bland · IEE Proceedings - Computers and Digital Techniques · 1997
The authors present a systolic design for a simple GA mechanism which provides high throughput and unidirectional pipelining by exploiting the inherent parallelism in the genetic operators. The design computes in O(N + G) time steps using O(N2) cells where N is the population size and G is the chromosome length. The area of the device is independent of the chromosome length and so can be easily scaled by replicating the arrays or by employing fine-grain migration. The array is generic in the sense that it does not rely on the fitness function and can be used as an accelerator for any GA application using uniform crossover between pairs of chromosomes. The design can also be used in hybrid systems as an add-on to complement existing designs and methods for fitness function acceleration and island-style population management.
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Christoph Schwarzweller · 1997
Although generic programming founds more and more attention -- nowadays generic programming languages as well as generic libraries exist -- there are hardly approaches for the verification of generic algorithms or generic libraries. This thesis deals with generic algorithms in the field of computer algebra. We propose the Mizar system as a theorem prover capable of verifying generic algorithms on an appropriate abstract level. The main advantage of the Mizar theorem prover is its special input language that enables textbook style presentation of proofs. For generic versions of Brown/Henrici addition and of Euclidan's algorithm we give complete correctness proofs written in the Mizar language. Moreover, we do not only prove algorithms correct in the usual sense. In addition we show how to check, using the Mizar system, that a generic algebraic algorithm is correctly instantiated with a particular domain. Answering this question that especially arises if one wants to implement generic programming languages, in the field of computer algebra requires non trival mathematical knowledge. To build a verification system using the Mizar theorem prover, we also implemented a generator which almost automatically computes for a given algorithm a set of theorems that imply the correctness of this algorithm.
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