K.-I. Ko. Complexitity Theory of Real Functions. Birkhauser, Boston, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....due to the presence of roundoff errors. Moreover, they are inappropriate for problems whose solution is sensitive to small variations on the input. As a consequence, exact real number computation has been advocated as an alternative solution (see e.g. 4, 5, 25] on the practical side and e.g. [2, 20, 21, 24, 26, 27, 28] on the foundational side) However, work on exact real number computation has focused on representations of real numbers and has neglected the issue of data types for real numbers. In particular, programming languages for exact real number computation with an explicit distinction between ....

K.-I. Ko. Complexitity Theory of Real Functions. Birkhauser, Boston, 1991.

....and the universality result follows. In order to obtain our definability results, we consider a domain equation like structure on the real numbers data type. The Real PCF notion of computability induces classical notions of computability on real numbers and real valued functions of real variables [3, 11, 12, 16, 19, 20], but this material is not included in this extended abstract due lack of space. Also, we only consider the unit interval type of Real PCF, although we indicate how the type for the whole real line can be handled. Contents 1 The real numbers domains 2 2 Effectively given coherent domains 5 3 ....

Ker-I Ko. Complexitity Theory of Real Functions. Birkhauser, Boston, 1991.

....map q. Then the result follows by taking g = f ffi q. 2.3 Computability For the purposes of this paper, a function f : Gamma1; 1] Gamma1; 1] is computable if it has a computable realizer OE : 3 3 . Computability on 3 can be defined e.g. via Turing machines with oracles [13,27,26]. In practice, an intuitive understanding of computability on 3 is enough for most purposes. 2.4 The lexicographical order and canonical forms We order numerals by the lexicographical order ff fi iff there is an integer k such that ff k fi k and ff i = fi i for each i k. Each number ....

Ker-I Ko. Complexitity Theory of Real Functions. Birkhauser, Boston, 1991.

....due to the presence of round off errors. Moreover, they are inappropriate for problems whose solution is sensitive to small variations on the input. As a consequence, exact real number computation has been advocated as an alternative solution (see e.g. 7, 8, 42] on the practical side and e.g. [5, 31, 32, 36, 43, 44, 45] on the foundational side) However, work on exact real number computation has focused on representations of real numbers and has neglected the issue of data types for real numbers. In particular, programming languages for exact real number computation with an explicit distinction between ....

Ker-I Ko. Complexitity Theory of Real Functions. Birkhauser, Boston, 1991.

....due to the presence of round off errors. Moreover, they are inappropriate for problems whose solution is sensitive to small variations on the input. As a consequence, exact real number computation has been advocated as an alternative solution (see e.g. 4, 5, 20] on the practical side and e.g. [2, 15, 16, 19, 21, 22, 23] on the foundational side) However, work on exact real number computation has focused on representations of real numbers and has neglected the issue of data types for real numbers. In particular, programming languages for exact real number computation with an explicit distinction between ....

Ker-I Ko. Complexitity Theory of Real Functions. Birkhauser, Boston, 1991.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC