11,801 research outputs found

    The logic of interactive Turing reduction

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    The paper gives a soundness and completeness proof for the implicative fragment of intuitionistic calculus with respect to the semantics of computability logic, which understands intuitionistic implication as interactive algorithmic reduction. This concept -- more precisely, the associated concept of reducibility -- is a generalization of Turing reducibility from the traditional, input/output sorts of problems to computational tasks of arbitrary degrees of interactivity. See http://www.cis.upenn.edu/~giorgi/cl.html for a comprehensive online source on computability logic

    Computation with Advice

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    Computation with advice is suggested as generalization of both computation with discrete advice and Type-2 Nondeterminism. Several embodiments of the generic concept are discussed, and the close connection to Weihrauch reducibility is pointed out. As a novel concept, computability with random advice is studied; which corresponds to correct solutions being guessable with positive probability. In the framework of computation with advice, it is possible to define computational complexity for certain concepts of hypercomputation. Finally, some examples are given which illuminate the interplay of uniform and non-uniform techniques in order to investigate both computability with advice and the Weihrauch lattice

    Evaluation of the Project Management Competences Based on the Semantic Networks

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    The paper presents the testing and evaluation facilities of the SinPers system. The SinPers is a web based learning environment in project management, capable of building and conducting a complete and personalized training cycle, from the definition of the learning objectives to the assessment of the learning results for each learner. The testing and evaluation facilities of SinPers system are based on the ontological approach. The educational ontology is mapped on a semantic network. Further, the semantic network is projected into a concept space graph. The semantic computability of the concept space graph is used to design the tests. The paper focuses on the applicability of the system in the certification, for the knowledge assessment, related to each element of competence. The semantic computability is used for differentiating between different certification levels.testing, assessment, ontology, semantic networks, certification.

    Finitely Generated Groups Are Universal

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    Universality has been an important concept in computable structure theory. A class C\mathcal{C} of structures is universal if, informally, for any structure, of any kind, there is a structure in C\mathcal{C} with the same computability-theoretic properties as the given structure. Many classes such as graphs, groups, and fields are known to be universal. This paper is about the class of finitely generated groups. Because finitely generated structures are relatively simple, the class of finitely generated groups has no hope of being universal. We show that finitely generated groups are as universal as possible, given that they are finitely generated: for every finitely generated structure, there is a finitely generated group which has the same computability-theoretic properties. The same is not true for finitely generated fields. We apply the results of this investigation to quasi Scott sentences

    On Computability and Triviality of Well Groups

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    The concept of well group in a special but important case captures homological properties of the zero set of a continuous map f:K→Rnf:K\to R^n on a compact space K that are invariant with respect to perturbations of f. The perturbations are arbitrary continuous maps within L∞L_\infty distance r from f for a given r>0. The main drawback of the approach is that the computability of well groups was shown only when dim K=n or n=1. Our contribution to the theory of well groups is twofold: on the one hand we improve on the computability issue, but on the other hand we present a range of examples where the well groups are incomplete invariants, that is, fail to capture certain important robust properties of the zero set. For the first part, we identify a computable subgroup of the well group that is obtained by cap product with the pullback of the orientation of R^n by f. In other words, well groups can be algorithmically approximated from below. When f is smooth and dim K<2n-2, our approximation of the (dim K-n)th well group is exact. For the second part, we find examples of maps f,f′:K→Rnf,f': K\to R^n with all well groups isomorphic but whose perturbations have different zero sets. We discuss on a possible replacement of the well groups of vector valued maps by an invariant of a better descriptive power and computability status.Comment: 20 pages main paper including bibliography, followed by 22 pages of Appendi
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