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• W1567753593 abstract "The distributive law known from arithmetics is one of the best tools for a computer scientist to grapple with the intractable nature of many applications. So, efficient algorithms have been developed for the computation of Fourier and Hadamard transforms, Bayesian networks, database queries, decoding problems and many more. The fact that they all benefit from the same technique suggests that a single generic algorithm must exist which solves all these problems efficiently. This essentially is the promise of local computation. The mathematical requirements for the application of local computation, which are clearly satisfied by the above examples, are pooled in an algebraic framework called valuation algebra. Moreover, this framework is general enough to be seen as an algebraic approach towards a definition of knowledge and information, since it perfectly reflects the adjudicated attributes of these notions. Our first contribution concerns a generalization of the valuation algebra framework that dispenses with the concept of neutral information. This solves the problem that in some formalisms, neutral elements do not have finite representations. Further, we also identify some valuation algebra instances that do not possess neutral information at all. From this generalized framework evolves the generic algorithm in the shape of the traditional local computation architectures. As an interesting side effect, we remark that some computations even become more efficient by the measures taken to renounce neutral information. A particular subclass of valuation algebras that is extensively studied in this thesis comprises formalisms that map configurations to semiring values. Besides the usefulness of this class to discover new valuation algebra instances, it will also be shown that they give rise to optimization problems under certain conditions. This insight motivated the development of a dynamic programming scheme for the identification of solution configurations that itself exploits local computation. Another far more powerful algorithm for the same task excels through innovation. By use of local computation, solution configurations are compiled into a Boolean function which is well suited to answer a large number of queries efficiently, that go far beyond the pure enumeration of solution configurations. In parallel to the theoretical considerations, we propose in this thesis a software framework containing generic implementations of the discussed algorithms. This system called NENOK is designed to be used as a service library for all kind of local computation related applications, but may also serve as an experimental workbench for educational purposes, since it provides a multiplicity of possibilities to inspect the local computation process. Additionally, it also takes an as yet disregarded aspect of information into consideration and realizes all local computation schemes as real distributed algorithms. This in turn raises new theoretical questions on how to ensure efficient communication during the computations, which are addressed theoretically and independently of the actual local computation architecture." @default.
• W1567753593 created "2016-06-24" @default.
• W1567753593 creator A5006356500 @default.
• W1567753593 date "2008-01-01" @default.
• W1567753593 modified "2023-09-26" @default.
• W1567753593 title "A generic framework for local computation" @default.
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