Name
Abstract | ||
|---|---|---|
We present a redevelopment of the theory of real-valued recursive functions that was introduced by C. Moore in 1996 by analogy with the standard formulation of the integer-valued recursive functions. While his work opened a new line of research on analog computation, the original paper contained some technical inaccuracies. We discuss possible attempts to remove the ambiguity in the behavior of the operators on partial functions, with a focus on his “primitive recursive” functions generated by the differential recursion operator that solves initial value problems. Under a reasonable reformulation, the functions in this class are shown to be analytic and computable in a strong sense in computable analysis. Despite this well-behavedness, the class turns out to be too big to have the originally purported relation to differentially algebraic functions, and hence to C. E. Shannon's model of analog computation. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1145/1507244.1507252 | ACM Trans. Comput. Log. |
Keywords | DocType | Volume |
real-valued recursive function,computable analysis,algebraic function,differentially algebraic functions,differential recursion operator,initial value problem,general terms: theory additional key words and phrases: analog computation,C. Moore,initial value problems,transcendentally transcendental functions,integer-valued recursive function,real recursive functions,C. E. Shannon,primitive recursive,analog computation | Journal | 10 |
Issue | ISSN | Citations |
3 | Revised and published in ACM Trans. Comput. Logic 10, Article 22,
2009, under the title "Differential Recursion". | 4 |
PageRank | References | Authors |
0.41 | 17 | 1 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Akitoshi Kawamura | 1 | 102 | 15.84 |