Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Exact Real Computer Arithmetic with Continued Fractions
IEEE Transactions on Computers
A domain-theoretic approach to computability on the real line
Theoretical Computer Science - Special issue on real numbers and computers
The Appearance of Big Integers in Exact Real Arithmetic Based on Linear Fractional Transformations
FoSSaCS '98 Proceedings of the First International Conference on Foundations of Software Science and Computation Structure
Semantics of Exact Real Arithmetic
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
From coinductive proofs to exact real arithmetic
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
Finite state transducers for modular möbius number systems
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
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This is an investigation into exact real number computation using the incremental approach of Potts (Ph.D. Thesis, Department of Computing, Imperial College, 1998), Edalat and Potts (Electronic Notes in Computer Science, Vol. 6, Elsevier Science Publishers, Amsterdam, 2000), Nielsen and Kornerup (J. Universal Comput. Sci. 1(7) (1995) 527), and Vuillemin (IEEE Trans. on Comput. 39(8) (1990) 1087) where numbers are represented as infinite streams of digits, each of which is a Möbius transformation. The objective is to determine for each particular system of digits which functions R → R can be computed by a finite transducer and ultimately to search for the most finitely expressible Möbius representations of real numbers. The main result is that locally such functions are either not continuously differentiable or equal to some Möbius transformation. This is proved using elementary properties of finite transition graphs and Möbius transformations. Applying the results to the standard signed-digit representations, we can classify functions that are finitely computable in such a representation and are continuously differentiable everywhere except for finitely many points. They are exactly those functions whose graph is a fractured line connecting finitely many points with rational coordinates.