Logical Approaches to Computational Barriers

On real primitive recursive functions and differential algebraicity

Speaker:
| Akitoshi Kawamura |

Slot: |
Array, 14:30-14:50, col. 4 |

In 1996 Moore introduced a class of real-valued "recursive" functions by analogy with Kleene's formulation of the classical recursion theory. While his concise characterization of the class offers unique insight into continuous-time computation and has inspired numerous subsequent works, technically it seems to suffer some gaps. In this informal talk I focus on his "primitive recursive" functions and try to specify the problem. In particular, I discuss possible attempts to remove the ambiguity in the behavior of the primitive recursion operator on partial functions. Different modifications keep different parts of the original claims, but it turns out that in any case the purported relation to differential algebraicity, and hence to Shannon's GPAC model, needs fix.

websites: Arnold Beckmann | 2006-05-03 |