caa a22 4500 44584289X CHVBK 20180317145350.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s11047-010-9229-6 doi (NATIONALLICENCE)springer-10.1007/s11047-010-9229-6 Durand-Lose Jérôme LIFO, Université d'Orléans, B.P. 6759, 45067, Orléans Cedex 2, France aut Abstract geometrical computation 5: embedding computable analysis [Elektronische Daten] [Jérôme Durand-Lose] Extended Signal machines are proven capable to compute any computable function in the understanding of recursive/computable analysis (CA), represented here with type-2 Turing machines (T2-TM) and signed binary. This relies on a mixed representation of any real number as an integer (in signed binary) plus an exact value in (−1, 1). This permits to have only finitely many signals present simultaneously. Extracting a (signed) bit, improving the precision by one bit and iterating a T2-TM only involve standard signal machines. For exact CA-computations, T2-TM have to deal with an infinite entry and to run through infinitely many iterations to produce an infinite output. This infinite duration can be provided by an infinite acceleration construction. Extracting/encoding an infinite sequence of bits is achieved as the limit of the approximation process with a careful handling of accumulations. Springer Science+Business Media B.V., 2010 Analog computation nationallicence Abstract geometrical computation nationallicence Computable analysis nationallicence Signal machine nationallicence Type-2 Turing machine nationallicence Natural Computing Springer Netherlands 10/4(2011-12-01), 1261-1273 1567-7818 10:4<1261 2011 10 11047 https://doi.org/10.1007/s11047-010-9229-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11047-010-9229-6 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Durand-Lose Jérôme LIFO, Université d'Orléans, B.P. 6759, 45067, Orléans Cedex 2, France aut NATIONALLICENCE 773 0- Natural Computing Springer Netherlands 10/4(2011-12-01), 1261-1273 1567-7818 10:4<1261 2011 10 11047 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer