<s>
A	O
Gödel	B-General_Concept
machine	I-General_Concept
is	O
a	O
hypothetical	O
self-improving	O
computer	B-Application
program	I-Application
that	O
solves	O
problems	O
in	O
an	O
optimal	O
way	O
.	O
</s>
<s>
The	O
Gödel	B-General_Concept
machine	I-General_Concept
is	O
often	O
discussed	O
when	O
dealing	O
with	O
issues	O
of	O
meta-learning	B-General_Concept
,	O
also	O
known	O
as	O
"	O
learning	O
to	O
learn.	O
"	O
</s>
<s>
Applications	O
include	O
automating	O
human	O
design	O
decisions	O
and	O
transfer	B-General_Concept
of	I-General_Concept
knowledge	I-General_Concept
between	O
multiple	O
related	O
tasks	O
,	O
and	O
may	O
lead	O
to	O
design	O
of	O
more	O
robust	O
and	O
general	O
learning	O
architectures	O
.	O
</s>
<s>
The	O
Gödel	B-General_Concept
machine	I-General_Concept
is	O
often	O
compared	O
with	O
Marcus	O
Hutter	O
's	O
AIXI	O
,	O
another	O
formal	O
specification	O
for	O
an	O
artificial	O
general	O
intelligence	O
.	O
</s>
<s>
Schmidhuber	O
points	O
out	O
that	O
the	O
Gödel	B-General_Concept
machine	I-General_Concept
could	O
start	O
out	O
by	O
implementing	O
AIXItl	O
as	O
its	O
initial	O
sub-program	O
,	O
and	O
self-modify	O
after	O
it	O
finds	O
proof	O
that	O
another	O
algorithm	O
for	O
its	O
search	O
code	O
will	O
be	O
better	O
.	O
</s>
<s>
Traditional	O
problems	O
solved	O
by	O
a	O
computer	O
only	O
require	O
one	O
input	B-General_Concept
and	O
provide	O
some	O
output	O
.	O
</s>
<s>
This	O
does	O
not	O
take	O
into	O
account	O
the	O
dynamic	O
natural	O
environment	O
,	O
and	O
thus	O
was	O
a	O
goal	O
for	O
the	O
Gödel	B-General_Concept
machine	I-General_Concept
to	O
overcome	O
.	O
</s>
<s>
The	O
Gödel	B-General_Concept
machine	I-General_Concept
has	O
limitations	O
of	O
its	O
own	O
,	O
however	O
.	O
</s>
<s>
Hence	O
even	O
a	O
Gödel	B-General_Concept
machine	I-General_Concept
with	O
unlimited	O
computational	O
resources	O
must	O
ignore	O
those	O
self-improvements	O
whose	O
effectiveness	O
it	O
cannot	O
prove	O
.	O
</s>
<s>
There	O
are	O
three	O
variables	O
that	O
are	O
particularly	O
useful	O
in	O
the	O
run	O
time	O
of	O
the	O
Gödel	B-General_Concept
machine	I-General_Concept
.	O
</s>
<s>
Any	O
input	B-General_Concept
meant	O
for	O
the	O
Gödel	B-General_Concept
machine	I-General_Concept
from	O
the	O
natural	O
environment	O
is	O
stored	O
in	O
variable	O
.	O
</s>
<s>
The	O
outputs	O
of	O
the	O
Gödel	B-General_Concept
machine	I-General_Concept
are	O
stored	O
in	O
variable	O
,	O
where	O
would	O
be	O
the	O
output	O
bit-string	O
at	O
some	O
time	O
.	O
</s>
<s>
Appends	O
the	O
n-th	O
axiom	B-Algorithm
as	O
a	O
theorem	O
to	O
the	O
current	O
theorem	O
sequence	O
.	O
</s>
<s>
Below	O
is	O
the	O
initial	O
axiom	B-Algorithm
scheme	O
:	O
</s>
<s>
Hardware	O
Axioms	B-Algorithm
formally	O
specify	O
how	O
components	O
of	O
the	O
machine	O
could	O
change	O
from	O
one	O
cycle	O
to	O
the	O
next	O
.	O
</s>
<s>
Reward	O
Axioms	B-Algorithm
define	O
the	O
computational	O
cost	O
of	O
hardware	O
instruction	O
and	O
the	O
physical	O
cost	O
of	O
output	O
actions	O
.	O
</s>
<s>
Related	O
Axioms	B-Algorithm
also	O
define	O
the	O
lifetime	O
of	O
the	O
Gödel	B-General_Concept
machine	I-General_Concept
as	O
scalar	O
quantities	O
representing	O
all	O
rewards/costs	O
.	O
</s>
<s>
Environment	O
Axioms	B-Algorithm
restrict	O
the	O
way	O
new	O
inputs	O
x	O
are	O
produced	O
from	O
the	O
environment	O
,	O
based	O
on	O
previous	O
sequences	O
of	O
inputs	O
y	O
.	O
</s>
<s>
Uncertainty	O
Axioms/String	O
Manipulation	O
Axioms	B-Algorithm
are	O
standard	O
axioms	B-Algorithm
for	O
arithmetic	O
,	O
calculus	O
,	O
probability	O
theory	O
,	O
and	O
string	O
manipulation	O
that	O
allow	O
for	O
the	O
construction	O
of	O
proofs	O
related	O
to	O
future	O
variable	O
values	O
within	O
the	O
Gödel	B-General_Concept
machine	I-General_Concept
.	O
</s>
<s>
Initial	O
State	O
Axioms	B-Algorithm
contain	O
information	O
about	O
how	O
to	O
reconstruct	O
parts	O
or	O
all	O
of	O
the	O
initial	O
state	O
.	O
</s>
<s>
Utility	O
Axioms	B-Algorithm
describe	O
the	O
overall	O
goal	O
in	O
the	O
form	O
of	O
utility	O
function	O
u	O
.	O
</s>
<s>
The	O
initial	O
input	B-General_Concept
to	O
the	O
Gödel	B-General_Concept
machine	I-General_Concept
is	O
the	O
representation	O
of	O
a	O
connected	O
graph	O
with	O
a	O
large	O
number	O
of	O
nodes	O
linked	O
by	O
edges	O
of	O
various	O
lengths	O
.	O
</s>
<s>
A	O
cognitive	B-General_Concept
robot	I-General_Concept
that	O
needs	O
at	O
least	O
1	O
liter	O
of	O
gasoline	O
per	O
hour	O
interacts	O
with	O
a	O
partially	O
unknown	O
environment	O
,	O
trying	O
to	O
find	O
hidden	O
,	O
limited	O
gasoline	O
depots	O
to	O
occasionally	O
refuel	O
its	O
tank	O
.	O
</s>
