## Abstract versus concrete computation on metric partial algebras (2004)

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Venue: | ACM Transactions on Computational Logic |

Citations: | 28 - 17 self |

### BibTeX

@ARTICLE{Tucker04abstractversus,

author = {J. V. Tucker},

title = {Abstract versus concrete computation on metric partial algebras},

journal = {ACM Transactions on Computational Logic},

year = {2004},

pages = {611--668}

}

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### Abstract

Data types containing infinite data, such as the real numbers, functions, bit streams and waveforms, are modelled by topological many-sorted algebras. In the theory of computation on topological algebras there is a considerable gap between so-called abstract and concrete models of computation. We prove theorems that bridge the gap in the case of metric algebras with partial operations. With an abstract model of computation on an algebra, the computations are invariant under isomorphisms and do not depend on any representation of the algebra. Examples of such models are the ‘while ’ programming language and the BCSS model. With a concrete model of computation, the computations depend on the choice of a representation of the algebra and are not invariant under isomorphisms. Usually, the representations are made from the set N of natural numbers, and computability is reduced to classical computability on N. Examples of such models are computability via effective metric spaces, effective domain representations, and type two enumerability. The theory of abstract models is stable: there are many models of computation, and