[PDF][PDF] Complexity in a type-1 framework for computable analysis
B Lambov - Giulia Battilotti, Paola Zizzi Logical Characterizations of …, 2005 - academia.edu
Giulia Battilotti, Paola Zizzi Logical Characterizations of PK and NPK …, 2005•academia.edu
Implementations of real number computations have largely been unusable in practice
because of the very bad performance ratio between them and machine precision floating
point numbers. Since a significant portion of the problem is the type-2 nature of the
computable analysis frameworks usually employed, this paper tries to address this by
creating a type-1 framework similar to the domain theoretic approach, with extensions that
permit us to reason about the complexity of real numbers and functions.
because of the very bad performance ratio between them and machine precision floating
point numbers. Since a significant portion of the problem is the type-2 nature of the
computable analysis frameworks usually employed, this paper tries to address this by
creating a type-1 framework similar to the domain theoretic approach, with extensions that
permit us to reason about the complexity of real numbers and functions.
Abstract
Implementations of real number computations have largely been unusable in practice because of the very bad performance ratio between them and machine precision floating point numbers. Since a significant portion of the problem is the type-2 nature of the computable analysis frameworks usually employed, this paper tries to address this by creating a type-1 framework similar to the domain theoretic approach, with extensions that permit us to reason about the complexity of real numbers and functions.
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