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CiE 2006 - Regular Talk: - On real primitive recursive functions and differential algebraicity
Computability in Europe 2006
Logical Approaches to Computational Barriers

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Regular Talk:
On real primitive recursive functions and differential algebraicity


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Speaker: Akitoshi Kawamura
Presentation: slide.pdf
Slot: Tue, 14:30-14:50, Faraday D (col. 4)

Abstract

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.


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