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Conference Papers Year : 2008

Abstract geometrical computation with accumulations: Beyond the Blum, Shub and Smale model

Abstract

Abstract geometrical computation (AGC) naturally arises as a continuous counterpart of cellular automata. It relies on signals (dimensionless points) traveling and colliding. It can carry out any Turing computation, but since it works with continuous time and space, some analog computing capability exists. In \textitAbstract Geometrical Computation and the Linear BSS Model (CiE 2007, LNCS 4497, p. 238-247), it is shown that AGC without any accumulation has the same computing capability as the linear BSS model. An accumulation brings infinitely many time steps in a finite duration. This has been used to implement the black-hole model of computation (Fundamenta Informaticae 74(4), p. 491-510). It also makes it possible to multiply two variables, thus simulating the full BSS. Nevertheless a BSS uncomputable function, the square root, can also be implemented, thus proving that the computing capability of AGC with isolated accumulations is strictly beyond the one of BSS.
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Dates and versions

hal-00448746 , version 1 (19-01-2010)

Identifiers

  • HAL Id : hal-00448746 , version 1

Cite

Jérôme Durand-Lose. Abstract geometrical computation with accumulations: Beyond the Blum, Shub and Smale model. 4th Conf. Computability in Europe (CiE~'08) (abstracts and extended abstracts of unpublished papers), 2008, Greece. pp.107--116. ⟨hal-00448746⟩
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