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Neural Networks and Computational Learning Theory

 

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NeuroCOLT Technical Report NC-TR-94-001

Computing over the Reals with Addition and Order: Higher Complexity Classes

Felipe Cucker and Pascal Koiran

Abstract
This paper deals with issues of structural complexity in a linear version of the Blum-Shub-Smale model of computation over the real numbers. Real versions of $\pspace$ and of the polynomial time hierarchy are defined, and their properties are investigated. Mainly two types of results are presented: Equivalence between quantification over the real numbers and over {0,1}; Characterizations of recognizable subsets of {0,1}^* in terms of familiar discrete complexity classes. The complexity of the decision and quantifier elimination problems in the theory of the reals with addition and order is also studied.

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