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    block this user Pascal Koiran Trusted member

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    Ecole Normale Superieure de Lyon, Computer Science Department, Lyon, France

    A Weak Version of the Blum, Shub & Smale Model

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    We propose a weak version of the Blum-Shub-Smale model of computation over the real numbers. In this weak model only a "moderate" usage of multiplications and divisions is allowed. The class of boolean languages recognizable in polynomial time is shown to be the complexity class P/poly. The main tool is a result on the existence of small rational points in semi-algebraic sets which is of independent interest. As an application, we generalize recent results of Siegelmann & Sontag on recurrent neural networks, and of Maass on feedforward nets. A preliminary version of this paper was presented at the 1993 IEEE Symposium on Foundations of Computer Science. Additional results include: Pi an efficient simulation of order-free real Turing machines by probabilistic Turing machines in the full Blum-Shub-Smale model; Pi an efficient simulation of arithmetic circuits over the integers by boolean circuits; Pi the strict inclusion of the real polynomial hierarchy in weak exponentia...

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    Title : A Weak Version of the Blum, Shub & Smale Model
    Abstract : We propose a weak version of the Blum-Shub-Smale model of computation over the real numbers. In this weak model only a "moderate" usage of multiplications and divisions is allowed. The class of boolean languages recognizable in polynomial time is shown to be the complexity class P/poly. The main tool is a result on the existence of small rational points in semi-algebraic sets which is of independent interest. As an application, we generalize recent results of Siegelmann & Sontag on recurrent neural networks, and of Maass on feedforward nets. A preliminary version of this paper was presented at the 1993 IEEE Symposium on Foundations of Computer Science. Additional results include: Pi an efficient simulation of order-free real Turing machines by probabilistic Turing machines in the full Blum-Shub-Smale model; Pi an efficient simulation of arithmetic circuits over the integers by boolean circuits; Pi the strict inclusion of the real polynomial hierarchy in weak exponentia...
    Subject : unspecified
    Area : Computer Science
    Language : English
    Affiliations : 
    Url : http://www.neurocolt.com/abs/1994/../../tech_reps/1994/nc-tr-94-005.ps.gz
    Doi : 10.1.1.28.2074

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    Pascal's Peer Evaluation activity

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    • Adrian Ebsary, Student, Master Level, University of Ottawa, McGill University.

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