## Computable Functions on Stream Algebras (1994)

Citations: | 12 - 8 self |

### BibTeX

@MISC{Tucker94computablefunctions,

author = {J.V. Tucker and Department Of Computer Science and J. I. Zucker},

title = {Computable Functions on Stream Algebras},

year = {1994}

}

### Years of Citing Articles

### OpenURL

### Abstract

. Let A be a many-sorted algebra. A stream over A is an infinite sequence of data from A. We study classes of computable functions on streams over A. We show how models of deterministic parallel computation on A can be adapted to provide new models of computation on stream algebras over A. The primary models considered are simultaneous primitive recursion schemes, with and without the least number operator, over A. We also look at an imperative model involving concurrent assignments. 1 Introduction We will address the problem of establishing the scope and limits of deterministic computing on many-sorted algebras with streams. 1.1 The problem For simplicity, suppose that A is a single sorted algebra, say A = (A; f 1 ; : : : ; f k ) where f i : A n(i) ! A is an operation, n(i) 0 and 1 i k. A stream is an infinite sequence ¸(0); ¸(1); : : : of data from A, represented by a function ¸ : N ! A. Let [N !A] be the set of all streams. We consider computing a mapping of the form f : [...