scholarly journals Formal Development of Distributed Enumeration Algorithms By Refinement-Based Techniques

10.29007/8n75 ◽  
2018 ◽  
Author(s):  
Maha Boussabbeh ◽  
Mohamed Tounsi ◽  
Ahmed Hadj Kacem ◽  
Mohamed Mosbah
Keyword(s):  
Distributed Algorithms ◽  
Main Idea ◽  
Top Down ◽  
Enumeration Algorithm ◽  
Modelling Language ◽  
Formal Development ◽  
Distributed Computations ◽  
Enumeration Problem ◽  
Enumeration Algorithms ◽  
Incremental Process

The enumeration problem addresses a collection of important algorithmic issues related to distributed computations. Among existing solutions, we are interested on the seminal algorithm of Mazurkiewicz, based on local computations. Our paper contributes to the design of a correct-by-construction enumeration algorithm. The main idea relies upon the development of the problem following a top/down approachthat can be supported by an incremental process controlled by the refinement of models. Event-B modelling language is supporting our methodological. Our main objective is to provide a verified component for distributed enumeration inorder to be used and extended for solving other problems of distributed algorithms.

scholarly journals A Comprehensive Study of the Key Enumeration Problem

Entropy ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 972 ◽  
Author(s):  
Ricardo Villanueva-Polanco
Keyword(s):  
Main Memory ◽  
Side Channel ◽  
Secret Key ◽  
Side Channel Attack ◽  
Enumeration Algorithm ◽  
Key Recovery ◽  
Recovery Algorithm ◽  
Enumeration Problem ◽  
Enumeration Algorithms ◽  
Recovery Problem

In this paper, we will study the key enumeration problem, which is connected to the key recovery problem posed in the cold boot attack setting. In this setting, an attacker with physical access to a computer may obtain noisy data of a cryptographic secret key of a cryptographic scheme from main memory via this data remanence attack. Therefore, the attacker would need a key-recovery algorithm to reconstruct the secret key from its noisy version. We will first describe this attack setting and then pose the problem of key recovery in a general way and establish a connection between the key recovery problem and the key enumeration problem. The latter problem has already been studied in the side-channel attack literature, where, for example, the attacker might procure scoring information for each byte of an Advanced Encryption Standard (AES) key from a side-channel attack and then want to efficiently enumerate and test a large number of complete 16-byte candidates until the correct key is found. After establishing such a connection between the key recovery problem and the key enumeration problem, we will present a comprehensive review of the most outstanding key enumeration algorithms to tackle the latter problem, for example, an optimal key enumeration algorithm (OKEA) and several nonoptimal key enumeration algorithms. Also, we will propose variants to some of them and make a comparison of them, highlighting their strengths and weaknesses.

Explaining Algorithms

2011 ◽  
pp. 2261-2279
Author(s):  
Tomasz Muldner ◽  
Elhadi Shakshuki
Keyword(s):  
Distance Education ◽  
Main Idea ◽  
Top Down ◽  
Levels Of Abstraction ◽  
Visualization System ◽  
Client Server ◽  
Novel Approach ◽  
Visualization Systems ◽  
Explanation System ◽  
Server Architecture

This article presents a novel approach for explaining algorithms that aims to overcome various pedagogical limitations of the current visualization systems. The main idea is that at any given time, a learner is able to focus on a single problem. This problem can be explained, studied, understood, and tested, before the learner moves on to study another problem. Toward this end, a visualization system that explains algorithms at various levels of abstraction has been designed and implemented. In this system, each abstraction is focused on a single operation from the algorithm using various media, including text and an associated visualization. The explanations are designed to help the user to understand basic properties of the operation represented by this abstraction, for example its invariants. The explanation system allows the user to traverse the hierarchy graph, using either a top-down (from primitive operations to general operations) approach or a bottom-up approach. Since the system is implemented using a client-server architecture, it can be used both in the classroom setting and through distance education.

scholarly journals Rotation Based MSS/MCS Enumeration

10.29007/8btb ◽  
2020 ◽  
Author(s):  
Jaroslav Bendík ◽  
Ivana Cerna
Keyword(s):  
Time Limit ◽  
Satisfiability Problem ◽  
Experimental Comparison ◽  
Boolean Formula ◽  
Enumeration Algorithm ◽  
Complete Enumeration ◽  
Enumeration Algorithms

Given an unsatisfiable Boolean Formula F in CNF, i.e., a set of clauses, one is often interested in identifying Maximal Satisfiable Subsets (MSSes) of F or, equivalently, the complements of MSSes called Minimal Correction Subsets (MCSes). Since MSSes (MC- Ses) find applications in many domains, e.g. diagnosis, ontologies debugging, or axiom pinpointing, several MSS enumeration algorithms have been proposed. Unfortunately, finding even a single MSS is often very hard since it naturally subsumes repeatedly solving the satisfiability problem. Moreover, there can be up to exponentially many MSSes, thus their complete enumeration is often practically intractable. Therefore, the algorithms tend to identify as many MSSes as possible within a given time limit. In this work, we present a novel MSS enumeration algorithm called RIME. Compared to existing algorithms, RIME is much more frugal in the number of performed satisfiability checks which we witness via an experimental comparison. Moreover, RIME is several times faster than existing tools.

Algorithm Education Using Structured Hypermedia

2011 ◽  
pp. 58-83
Author(s):  
Tomasz Müldner ◽  
Elhadi Shakshuki ◽  
Andreas Kerren
Keyword(s):  
Distance Education ◽  
Computer Science ◽  
Main Idea ◽  
Completion Rate ◽  
Top Down ◽  
Levels Of Abstraction ◽  
New Approach ◽  
Client Server ◽  
Visualization Systems ◽  
Server Architecture

Understanding of algorithms is one of the most challenging aspects of the study of computer science. Over two decades of research has been devoted to improving techniques to learn and teach algorithms. In this work, we present a new approach for explaining algorithms that aims to overcome various pedagogical limitations of the current visualization systems. The main idea is that, at any given time, a learner is able to focus on a single problem. This problem can be explained, studied, understood, and tested before the learner moves on to study another problem. The structured hypermedia algorithm explanation (SHALEX) system is the system we designed and implemented to explain algorithms at various levels of abstraction. In this system, each abstraction is focused on a single operation from the algorithm using various media, including text and an associated visualization. The explanations are designed to help the user to understand basic properties of the operation represented by this abstraction, for example its invariants. SHALEX allows the user to traverse the graph-based algorithm model, using a top-down (from primitive operations to general operations) approach, a bottom-up approach, or a mix of these two approaches. Since the system is implemented using a client-server architecture, it can be used both through distance education and in the classroom setting. To aid and monitor the leaner, we also developed an agent in SHALEX that provides help and monitors the completion rate.

A New Algorithm for the Single Source Weber Problem with Limited Distances

2021 ◽  
Vol 55 (5) ◽  
pp. 1136-1150
Author(s):  
Giovanni Righini
Keyword(s):  
Time Complexity ◽  
Location Theory ◽  
Continuous Optimization ◽  
Intersection Point ◽  
Weber Problem ◽  
Single Source ◽  
Enumeration Algorithm ◽  
Worst Case ◽  
Enumeration Algorithms ◽  
Pass Through

The single source Weber problem with limited distances (SSWPLD) is a continuous optimization problem in location theory. The SSWPLD algorithms proposed so far are based on the enumeration of all regions of [Formula: see text] defined by a given set of n intersecting circumferences. Early algorithms require [Formula: see text] time for the enumeration, but they were recently shown to be incorrect in case of degenerate intersections, that is, when three or more circumferences pass through the same intersection point. This problem was fixed by a modified enumeration algorithm with complexity [Formula: see text], based on the construction of neighborhoods of degenerate intersection points. In this paper, it is shown that the complexity for correctly dealing with degenerate intersections can be reduced to [Formula: see text] so that existing enumeration algorithms can be fixed without increasing their [Formula: see text] time complexity, which is due to some preliminary computations unrelated to intersection degeneracy. Furthermore, a new algorithm for enumerating all regions to solve the SSWPLD is described: its worst-case time complexity is [Formula: see text]. The new algorithm also guarantees that the regions are enumerated only once.

ENUMERATING THE k-TANGLE PROJECTIONS

2012 ◽  
Vol 21 (07) ◽  
pp. 1250069 ◽  
Author(s):  
ANDREY BOGDANOV ◽  
VADIM MESHKOV ◽  
ALEXANDER OMELCHENKO ◽  
MIKHAIL PETROV
Keyword(s):  
Enumeration Algorithm ◽  
Enumeration Problem

The paper addresses the enumeration problem for k-tangles. We introduce the notion of a cascade diagram of a k-tangle projection and suggest an effective enumeration algorithm for projections based on the cascade representation. Tangle projections and alternating tangles with up to 12 crossings are tabulated. We also provide pictures of alternating k-tangles with at most five crossings.

scholarly journals Revisiting snapshot algorithms by refinement-based techniques

2014 ◽  
Vol 11 (1) ◽  
pp. 251-270 ◽  
Author(s):  
Bruno Andriamiarina ◽  
Dominique Méry ◽  
Kumar Singh
Keyword(s):  
Distributed System ◽  
Distributed Algorithms ◽  
Distributed Algorithm ◽  
Modeling Language ◽  
Distributed Programs ◽  
Incremental Development ◽  
Distributed Computations

The snapshot problem addresses a collection of important algorithmic issues related to distributed computations, which are used for debugging or recovering distributed programs. Among existing solutions, Chandy and Lamport have proposed a simple distributed algorithm. In this paper, we explore the correct-byconstruction process to formalize the snapshot algorithms in distributed system. The formalization process is based on a modeling language Event B, which supports a refinement-based incremental development using RODIN platform. These refinement-based techniques help to derive correct distributed algorithms. Moreover, we demonstrate how other distributed algorithms can be revisited. A consequence is to provide a fully mechanized proof of the resulting distributed algorithms.

scholarly journals Completely top–down hierarchical structure in quantum mechanics

2018 ◽  
Vol 115 (46) ◽  
pp. 11730-11735 ◽  
Author(s):  
Yakir Aharonov ◽  
Eliahu Cohen ◽  
Jeff Tollaksen
Keyword(s):  
Quantum Mechanics ◽  
Lower Order ◽  
Inductive Reasoning ◽  
Main Idea ◽  
Higher Order ◽  
Specific Class ◽  
Strong Correlations ◽  
Many Body ◽  
Top Down ◽  
Quantum Mechanical Systems

Can a large system be fully characterized using its subsystems via inductive reasoning? Is it possible to completely reduce the behavior of a complex system to the behavior of its simplest “atoms”? In this paper we answer these questions in the negative for a specific class of systems and measurements. After a general introduction of the topic, we present the main idea with a simple two-particle example, where strong correlations arise between two apparently empty boxes. This leads to surprising effects within atomic and electromagnetic systems. A general construction based on pre- and postselected ensembles is then suggested, wherein the N-body correlation can be genuinely perceived as a global property, as long as one is limited to performing measurements which we term “strictly local.” We conclude that under certain boundary conditions, higher-order correlations within quantum mechanical systems can determine lower-order ones, but not vice versa. Surprisingly, the lower-order correlations provide no information whatsoever regarding the higher-order correlations. This supports a top–down structure in many-body quantum mechanics.

scholarly journals Laws, causation and dynamics at different levels

2011 ◽  
Vol 2 (1) ◽  
pp. 101-114 ◽  
Author(s):  
Jeremy Butterfield
Keyword(s):  
Dynamical Systems ◽  
Systems Theory ◽  
Main Idea ◽  
Coarse Graining ◽  
Dynamical Systems Theory ◽  
Main Task ◽  
Top Down ◽  
Different Levels

I have two main aims. The first is general, and more philosophical (§2). The second is specific, and more closely related to physics (§§3 and 4). The first aim is to state my general views about laws and causation at different ‘levels’. The main task is to understand how the higher levels sustain notions of law and causation that ‘ride free’ of reductions to the lower level or levels. I endeavour to relate my views to those of other symposiasts. The second aim is to give a framework for describing dynamics at different levels, emphasizing how the various levels' dynamics can mesh or fail to mesh. This framework is essentially that of elementary dynamical systems theory. The main idea will be, for simplicity, to work with just two levels, dubbed ‘micro’ and ‘macro’, which are related by coarse-graining. I use this framework to describe, in part, the first four of Ellis' five types of top-down causation.

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