test FOO test
Computability in Europe 2006
Logical Approaches to Computational Barriers
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