<s>
A	O
queue	B-Application
machine	I-Application
,	O
queue	B-Application
automaton	I-Application
,	O
or	O
pullup	O
automaton	O
(	O
PUA	O
)	O
is	O
a	O
finite	B-Architecture
state	I-Architecture
machine	I-Architecture
with	O
the	O
ability	O
to	O
store	O
and	O
retrieve	O
data	O
from	O
an	O
infinite-memory	O
queue	B-Application
.	O
</s>
<s>
It	O
is	O
a	O
model	O
of	O
computation	O
equivalent	O
to	O
a	O
Turing	B-Architecture
machine	I-Architecture
,	O
and	O
therefore	O
it	O
can	O
process	O
the	O
same	O
class	O
of	O
formal	O
languages	O
.	O
</s>
<s>
is	O
the	O
finite	O
queue	B-Application
alphabet	O
;	O
</s>
<s>
is	O
the	O
initial	O
queue	B-Application
symbol	O
;	O
</s>
<s>
is	O
the	O
start	B-Architecture
state	I-Architecture
;	O
</s>
<s>
A	O
machine	O
configuration	O
is	O
an	O
ordered	O
pair	O
of	O
its	O
state	O
and	O
queue	B-Application
contents	O
,	O
where	O
denotes	O
the	O
Kleene	O
closure	O
of	O
.	O
</s>
<s>
where	O
is	O
a	O
symbol	O
from	O
the	O
queue	B-Application
alphabet	O
,	O
is	O
a	O
sequence	O
of	O
queue	B-Application
symbols	O
(	O
)	O
,	O
and	O
.	O
</s>
<s>
Note	O
the	O
"	O
first-in-first-out	O
"	O
property	O
of	O
the	O
queue	B-Application
in	O
the	O
relation	O
.	O
</s>
<s>
We	O
can	O
prove	O
that	O
a	O
queue	B-Application
machine	I-Application
is	O
equivalent	O
to	O
a	O
Turing	B-Architecture
machine	I-Architecture
by	O
showing	O
that	O
a	O
queue	B-Application
machine	I-Application
can	O
simulate	O
a	O
Turing	B-Architecture
machine	I-Architecture
and	O
vice	O
versa	O
.	O
</s>
<s>
A	O
Turing	B-Architecture
machine	I-Architecture
can	O
be	O
simulated	O
by	O
a	O
queue	B-Application
machine	I-Application
that	O
keeps	O
a	O
copy	O
of	O
the	B-Architecture
Turing	I-Architecture
machine	I-Architecture
's	O
contents	O
in	O
its	O
queue	B-Application
at	O
all	O
times	O
,	O
with	O
two	O
special	O
markers	O
:	O
one	O
for	O
the	B-Architecture
Turing	I-Architecture
machine	I-Architecture
's	O
head	O
position	O
,	O
and	O
one	O
for	O
the	O
end	O
of	O
the	O
tape	O
;	O
its	O
transitions	O
simulate	O
those	O
of	O
the	B-Architecture
Turing	I-Architecture
machine	I-Architecture
by	O
running	O
through	O
the	O
whole	O
queue	B-Application
,	O
popping	O
off	O
each	O
of	O
its	O
symbols	O
and	O
re-enqueing	O
either	O
the	O
popped	O
symbol	O
,	O
or	O
,	O
near	O
the	O
head	O
position	O
,	O
the	O
equivalent	O
of	O
the	B-Architecture
Turing	I-Architecture
machine	I-Architecture
transition	O
's	O
effect	O
.	O
</s>
<s>
A	O
queue	B-Application
machine	I-Application
can	O
be	O
simulated	O
by	O
a	O
Turing	B-Architecture
machine	I-Architecture
,	O
but	O
more	O
easily	O
by	O
a	O
multi-tape	B-Application
Turing	I-Application
machine	I-Application
,	O
which	O
is	O
known	O
to	O
be	O
equivalent	O
to	O
a	O
normal	O
single-tape	O
machine	O
.	O
</s>
<s>
The	O
simulating	O
queue	B-Application
machine	I-Application
reads	O
input	O
on	O
one	O
tape	O
and	O
stores	O
the	O
queue	B-Application
on	O
the	O
second	O
,	O
with	O
pushes	O
and	O
pops	O
defined	O
by	O
simple	O
transitions	O
to	O
the	O
beginning	O
and	O
end	O
symbols	O
of	O
the	O
tape	O
.	O
</s>
<s>
Queue	B-Application
machines	I-Application
offer	O
a	O
simple	O
model	O
on	O
which	O
to	O
base	O
computer	B-General_Concept
architectures	I-General_Concept
,	O
programming	O
languages	O
,	O
or	O
algorithms	O
.	O
</s>
