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From coinductive proofs to exact real arithmetic
"... Abstract. We give a coinductive characterisation of the set of continuous functions defined on a compact real interval, and extract certified programs that construct and combine exact real number algorithms with respect to the binary signed digit representation of real numbers. The data type corresp ..."
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Abstract. We give a coinductive characterisation of the set of continuous functions defined on a compact real interval, and extract certified programs that construct and combine exact real number algorithms with respect to the binary signed digit representation of real numbers. The data type corresponding to the coinductive definition of continuous functions consists of finitely branching nonwellfounded trees describing when the algorithm writes and reads digits. This is a pilot study in using prooftheoretic methods for obtaining certified algorithms in exact real arithmetic. 1
12345efghi UNIVERSITY OF WALES SWANSEA REPORT SERIES
"... Computability on topological spaces via domain representations by V StoltenbergHansen and J V Tucker Report # CSR 22007Computability on topological spaces via domain representations ..."
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Computability on topological spaces via domain representations by V StoltenbergHansen and J V Tucker Report # CSR 22007Computability on topological spaces via domain representations
THE JOURNAL OF LOGIC AND ALGEBRAIC PROGRAMMING
, 2005
"... www.elsevier.com/locate/jlap Exact real arithmetic using centred intervals and bounded error terms ..."
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www.elsevier.com/locate/jlap Exact real arithmetic using centred intervals and bounded error terms
This work is licensed under the Creative Commons Attribution License. Computational Complexity of Iterated Maps on the Interval
"... The exact computation of orbits of discrete dynamical systems on the interval is considered. Therefore, a multipleprecision floating point approach based on error analysis is chosen and a general algorithm is presented. The correctness of the algorithm is shown and the computational complexity is ..."
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The exact computation of orbits of discrete dynamical systems on the interval is considered. Therefore, a multipleprecision floating point approach based on error analysis is chosen and a general algorithm is presented. The correctness of the algorithm is shown and the computational complexity is analyzed. As a main result, the computational complexity measure considered here is related to the Ljapunow exponent of the dynamical system under consideration. 1