January 2011
Intermediate to advanced
192 pages
5h 34m
English
Content preview from Computability Theory
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70 Computability Theory
where as usual “=” means that either both sides are undefined or else both sides are
defined and equal.
In other words, we can break down the calculation of [[e]](x) into four steps:
l
Find t
halt
= µt T(e, x, t).
l
Find the terminal snapshot snap
halt
= snap(e, x, t
halt
).
l
Find the memory number m
halt
= (snap
halt
)
1
.
l
Find the output value (m
halt
)
∗
0
.
The first step uses a general recursive function; the other steps use primitive recursive
functions.
It is straightforward to extend these ideas to functions of more than one variable:
snap
(2)
(e, x
1
, x
2
, t) is obtained by starting with
snap
(2)
(e, x
1
, x
2
, 0) = [0, 3
x
1
· 5
x
2
]
and proceeding as before. ...
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