Relative Computability Article Index for
Relative
Website Links For
Relative
 

Information About

Relative Computability




The first formal definition of relative computability, then called relative reducibility, was given by Alan Turing in 1939 in terms of Oracle Machine s. Later in 1943 and 1952 Stephen Kleene defined an equivalent concept in terms of Recursive Function s. In 1948 Emil Post extended his Canonical System s to define a similar concept.


DEFINITION


Given a set of Natural Number s ''A'', a function
:f: A \subseteq \mathbb{N} o \mathbb{N}
is called ''A''-computable if there exists an Oracle Machine with an oracle for ''A'' which can compute ''f''.

A set ''B'' is called ''A''-recursive if its Indicator Function 1''B'' is ''A''-computable.


EXAMPLES




SEE ALSO




REFERENCES


  • 2 (1996), 284-321.