965 resultados para Algebra, Boolean.


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More and more traditional manufacturing companies form or join inter-organizational networks to bundle their physical products with related services to offer superior value propositions to their customers. Some of these product-related services can be digitized completely and thus fully delivered electronically. Other services require the physical integration of external factors, but can still be coordinated electronically. In both cases companies and consumers face the problem of discovering appropriate product-related service offerings in the network or market. Based on ideas from the web service discovery discipline we propose a meet-in-the-middle approach between heavy-weight semantic technologies and simple boolean search to address this issue. Our approach is able to consider semantic relations in service descriptions and queries and thus delivers better results than syntax-based search. However – unlike most semantic approaches – it does not require the use of any formal language for semantic markup and thus requires less resources and skills for both service providers and consumers. To fully realize the potentials of the proposed approach a domain ontology is needed. In this research-in-progress paper we construct such an ontology for the domain of product-service bundles through analysis and synthesis of related work on service description. This will serve as an anchor for future research to iteratively improve and evaluate the ontology through collaborative design efforts and practical application.

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Analysis of behavioural consistency is an important aspect of software engineering. In process and service management, consistency verification of behavioural models has manifold applications. For instance, a business process model used as system specification and a corresponding workflow model used as implementation have to be consistent. Another example would be the analysis to what degree a process log of executed business operations is consistent with the corresponding normative process model. Typically, existing notions of behaviour equivalence, such as bisimulation and trace equivalence, are applied as consistency notions. Still, these notions are exponential in computation and yield a Boolean result. In many cases, however, a quantification of behavioural deviation is needed along with concepts to isolate the source of deviation. In this article, we propose causal behavioural profiles as the basis for a consistency notion. These profiles capture essential behavioural information, such as order, exclusiveness, and causality between pairs of activities of a process model. Consistency based on these profiles is weaker than trace equivalence, but can be computed efficiently for a broad class of models. In this article, we introduce techniques for the computation of causal behavioural profiles using structural decomposition techniques for sound free-choice workflow systems if unstructured net fragments are acyclic or can be traced back to S- or T-nets. We also elaborate on the findings of applying our technique to three industry model collections.

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Two newspaper numbers games based on simple arithmetic relationships are discussed. One is rather trivial, but very useful as an introduction to the second, whose potential to give students of elementary algebra practice in semi ad-hoc reasoning and to build general arithmetic reasoning skills was explored theoretically in an earlier paper. Preliminary results on the effectiveness of this general approach are presented, with student performance and feedback on an assignment task and formal examination included, and recommendations for future work.

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This paper presents a control design for tracking of attitude and speed of an underactuated slender-hull unmanned underwater vehicle (UUV). The control design is based on Port-Hamiltonian theory. The target dynamics (desired dynamic response) is shaped with particular attention to the target mass matrix so that the influence of the unactuated dynamics on the controlled system is suppressed. This results in achievable dynamics independent of uncontrolled states. Throughout the design, insight of the physical phenomena involved is used to propose the desired target dynamics. The performance of the design is demonstrated through simulation with a high-fidelity model.

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A newspaper numbers game based on simple arithmetic relationships is discussed. Its potential to give students of elementary algebra practice in semi-ad hoc reasoning and to build general arithmetic reasoning skills is explored.

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The five quantities of interest in elementary finance problems are present value, future value, amount of periodic payment, number of periods and the rate of compound interest per period. A recursive approach to computing each of these five quantities in a modern version of Excel, for the case of ordinary annuities, is described. The aim is to increase student understanding and build confidence in the answer obtained, and this may be achieved with only linear relationships and in cases where student knowledge of algebra is essentially zero. Annuity problems may be solved without use of logarithms and black-box intrinsic functions; these being used only as check mechanisms. The author has had success with the method at Bond University and surrounding high schools in Queensland, Australia.

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Modular arithmetic has often been regarded as something of a mathematical curiosity, at least by those unfamiliar with its importance to both abstract algebra and number theory, and with its numerous applications. However, with the ubiquity of fast digital computers, and the need for reliable digital security systems such as RSA, this important branch of mathematics is now considered essential knowledge for many professionals. Indeed, computer arithmetic itself is, ipso facto, modular. This chapter describes how the modern graphical spreadsheet may be used to clearly illustrate the basics of modular arithmetic, and to solve certain classes of problems. Students may then gain structural insight and the foundations laid for applications to such areas as hashing, random number generation, and public-key cryptography.

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New criteria of extended resiliency and extended immunity of vectorial Boolean functions, such as S-boxes for stream or block ciphers, were recently introduced. They are related to a divide-and-conquer approach to algebraic attacks by conditional or unconditional equations. Classical resiliency turns out to be a special case of extended resiliency and as such requires more conditions to be satisfied. In particular, the algebraic degrees of classically resilient S-boxes are restricted to lower values. In this paper, extended immunity and extended resiliency of S-boxes are studied and many characterisations and properties of such S-boxes are established. The new criteria are shown to be necessary and sufficient for resistance against the divide-and-conquer algebraic attacks by conditional or unconditional equations.

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We consider secret sharing with binary shares. This model allows us to use the well developed theory of cryptographically strong boolean functions. We prove that for given secret sharing, the average cheating probability over all cheating and original vectors, i.e., ρ ¯= 1 n ⋅ 2 −n ∑ n c=1 ∑ α∈Vn ρ c,α , satisfies ρ ¯⩾ 1 2 , and the equality holds ⇔ ρc,α satisfies ρc,α = 1/2 for every cheating vector δc and every original vector α. In this case the secret sharing is said to be cheating immune. We further establish a relationship between cheating-immune secret sharing and cryptographic criteria of boolean functions. This enables us to construct cheating-immune secret sharing.

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This research proposes the development of interfaces to support collaborative, community-driven inquiry into data, which we refer to as Participatory Data Analytics. Since the investigation is led by local communities, it is not possible to anticipate which data will be relevant and what questions are going to be asked. Therefore, users have to be able to construct and tailor visualisations to their own needs. The poster presents early work towards defining a suitable compositional model, which will allow users to mix, match, and manipulate data sets to obtain visual representations with little-to-no programming knowledge. Following a user-centred design process, we are subsequently planning to identify appropriate interaction techniques and metaphors for generating such visual specifications on wall-sized, multi-touch displays.

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The paper investigates the design of secret sharing that is immune against cheating (as defined by the Tompa-Woll attack). We examine secret sharing with binary shares and secrets. Bounds on the probability of successful cheating are given for two cases. The first case relates to secret sharing based on bent functions and results in a non-perfect scheme. The second case considers perfect secret sharing built on highly nonlinear balanced Boolean functions.

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Algebraic immunity AI(f) defined for a boolean function f measures the resistance of the function against algebraic attacks. Currently known algorithms for computing the optimal annihilator of f and AI(f) are inefficient. This work consists of two parts. In the first part, we extend the concept of algebraic immunity. In particular, we argue that a function f may be replaced by another boolean function f^c called the algebraic complement of f. This motivates us to examine AI(f ^c ). We define the extended algebraic immunity of f as AI *(f)= min {AI(f), AI(f^c )}. We prove that 0≤AI(f)–AI *(f)≤1. Since AI(f)–AI *(f)= 1 holds for a large number of cases, the difference between AI(f) and AI *(f) cannot be ignored in algebraic attacks. In the second part, we link boolean functions to hypergraphs so that we can apply known results in hypergraph theory to boolean functions. This not only allows us to find annihilators in a fast and simple way but also provides a good estimation of the upper bound on AI *(f).

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The paper addresses the cheating prevention in secret sharing. We consider secret sharing with binary shares. The secret also is binary. This model allows us to use results and constructions from the well developed theory of cryptographically strong boolean functions. In particular, we prove that for given secret sharing, the average cheating probability over all cheating vectors and all original vectors, i.e., 1/n 2n ∑c=1...n ∑α∈V n ρc,α , denoted by ρ, satisfies ρ ≥ ½, and the equality holds if and only if ρc,α satisfies ρc,α= ½ for every cheating vector δc and every original vector α. In this case the secret sharing is said to be cheating immune. We further establish a relationship between cheating-immune secret sharing and cryptographic criteria of boolean functions.This enables us to construct cheating-immune secret sharing.

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A unit cube in k-dimension (or a k-cube) is defined as the Cartesian product R-1 x R-2 x ... x R-k, where each R-i is a closed interval on the real line of the form [a(j), a(i), + 1]. The cubicity of G, denoted as cub(G), is the minimum k such that G is the intersection graph of a collection of k-cubes. Many NP-complete graph problems can be solved efficiently or have good approximation ratios in graphs of low cubicity. In most of these cases the first step is to get a low dimensional cube representation of the given graph. It is known that for graph G, cub(G) <= left perpendicular2n/3right perpendicular. Recently it has been shown that for a graph G, cub(G) >= 4(Delta + 1) In n, where n and Delta are the number of vertices and maximum degree of G, respectively. In this paper, we show that for a bipartite graph G = (A boolean OR B, E) with |A| = n(1), |B| = n2, n(1) <= n(2), and Delta' = min {Delta(A),Delta(B)}, where Delta(A) = max(a is an element of A)d(a) and Delta(B) = max(b is an element of B) d(b), d(a) and d(b) being the degree of a and b in G, respectively , cub(G) <= 2(Delta' + 2) bar left rightln n(2)bar left arrow. We also give an efficient randomized algorithm to construct the cube representation of G in 3 (Delta' + 2) bar right arrowIn n(2)bar left arrow dimension. The reader may note that in general Delta' can be much smaller than Delta.

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This paper presents a novel algebraic formulation of the central problem of screw theory, namely the determination of the principal screws of a given system. Using the algebra of dual numbers, it shows that the principal screws can be determined via the solution of a generalised eigenproblem of two real, symmetric matrices. This approach allows the study of the principal screws of the general two-, three-systems associated with a manipulator of arbitrary geometry in terms of closed-form expressions of its architecture and configuration parameters. We also present novel methods for the determination of the principal screws for four-, five-systems which do not require the explicit computation of the reciprocal systems. Principal screws of the systems of different orders are identified from one uniform criterion, namely that the pitches of the principal screws are the extreme values of the pitch.The classical results of screw theory, namely the equations for the cylindroid and the pitch-hyperboloid associated with the two-and three-systems, respectively have been derived within the proposed framework. Algebraic conditions have been derived for some of the special screw systems. The formulation is also illustrated with several examples including two spatial manipulators of serial and parallel architecture, respectively.