Complexity spaces as quantitative domains of computation |
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Authors: | S Romaguera MP Schellekens |
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Institution: | a Instituto de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, 46071 Valencia, Spain b Center of Efficiency-Oriented Languages, Department of Computer Science, University College Cork, Western Road, Cork, Ireland c Departamento de Ciencias Matemáticas e Informática, Universidad de las Islas Baleares, 07122 Palma, Spain |
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Abstract: | We study domain theoretic properties of complexity spaces. Although the so-called complexity space is not a domain for the usual pointwise order, we show that, however, each pointed complexity space is an ω-continuous domain for which the complexity quasi-metric induces the Scott topology, and the supremum metric induces the Lawson topology. Hence, each pointed complexity space is both a quantifiable domain in the sense of M. Schellekens and a quantitative domain in the sense of P. Waszkiewicz, via the partial metric induced by the complexity quasi-metric. |
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Keywords: | Complexity space Pointed Continuous domain Scott topology Quantitative domain |
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