Abstract:

A Kleene's Theory of Real Valued Functions
 
We explain from very basic notions how a theory of recursive real
valued functions can be developed. Besides its mathematical contents,
we foresee many interesting applications either in the theory of
dynamical systems either in classical computability and complexity
theories.
 
Many aspects of this research have been presented in several
conferences and workshops, but the very crucial notions, e.g. of
iteration, of simulation of Turing machines by differential
equations, of representation of classical complexity classes, of
relations with hyperarithmetical and analytical hierarchies are
somewhat not known to a reasonable percentage of computer scientists,
not to say almost all.
 
It is our main motivation to show how elegant this theory can get,
how fruitful and how simple it can be made (with first conceps of
mathematics).
 

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J. Felix Costa
Departamento de Matematica
Instituto Superior Tecnico
Av. Rovisco Pais, 1049-001 Lisboa, PORTUGAL
tel:      351 - 21 - 841 71 45
fax:     351 - 21 - 841 75 98
e-mail:   fgc@math.ist.utl.pt
www:    http://fgc.math.ist.utl.pt/jfc.htm
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