<s>
In	O
computer	B-General_Concept
science	I-General_Concept
,	O
a	O
linear	B-Application
bounded	I-Application
automaton	I-Application
(	O
plural	O
linear	B-Application
bounded	I-Application
automata	I-Application
,	O
abbreviated	O
LBA	O
)	O
is	O
a	O
restricted	O
form	O
of	O
Turing	B-Architecture
machine	I-Architecture
.	O
</s>
<s>
A	O
linear	B-Application
bounded	I-Application
automaton	I-Application
is	O
a	O
nondeterministic	O
Turing	B-Architecture
machine	I-Architecture
that	O
satisfies	O
the	O
following	O
three	O
conditions	O
:	O
</s>
<s>
Like	O
a	O
Turing	B-Architecture
machine	I-Architecture
,	O
an	O
LBA	O
possesses	O
a	O
tape	O
made	O
up	O
of	O
cells	O
that	O
can	O
contain	O
symbols	O
from	O
a	O
finite	O
alphabet	O
,	O
a	O
head	O
that	O
can	O
read	O
from	O
or	O
write	O
to	O
one	O
cell	O
on	O
the	O
tape	O
at	O
a	O
time	O
and	O
can	O
be	O
moved	O
,	O
and	O
a	O
finite	O
number	O
of	O
states	O
.	O
</s>
<s>
An	O
LBA	O
differs	O
from	O
a	O
Turing	B-Architecture
machine	I-Architecture
in	O
that	O
while	O
the	O
tape	O
is	O
initially	O
considered	O
to	O
have	O
unbounded	O
length	O
,	O
only	O
a	O
finite	O
contiguous	O
portion	O
of	O
the	O
tape	O
,	O
whose	O
length	O
is	O
a	O
linear	O
function	O
of	O
the	O
length	O
of	O
the	O
initial	O
input	O
,	O
can	O
be	O
accessed	O
by	O
the	O
read/write	O
head	O
;	O
hence	O
the	O
name	O
linear	B-Application
bounded	I-Application
automaton	I-Application
.	O
</s>
<s>
This	O
limitation	O
makes	O
an	O
LBA	O
a	O
somewhat	O
more	O
accurate	O
model	O
of	O
a	O
real-world	O
computer	O
than	O
a	O
Turing	B-Architecture
machine	I-Architecture
,	O
whose	O
definition	O
assumes	O
unlimited	O
tape	O
.	O
</s>
<s>
Linear	B-Application
bounded	I-Application
automata	I-Application
are	O
acceptors	O
for	O
the	O
class	O
of	O
context-sensitive	O
languages	O
.	O
</s>
<s>
In	O
1960	O
,	O
John	O
Myhill	O
introduced	O
an	O
automaton	O
model	O
today	O
known	O
as	O
deterministic	O
linear	B-Application
bounded	I-Application
automaton	I-Application
.	O
</s>
<s>
Kuroda	O
introduced	O
the	O
more	O
general	O
model	O
of	O
(	O
nondeterministic	O
)	O
linear	B-Application
bounded	I-Application
automata	I-Application
,	O
and	O
adapted	O
Landweber	O
's	O
proof	O
to	O
show	O
that	O
the	O
languages	O
accepted	O
by	O
nondeterministic	O
linear	B-Application
bounded	I-Application
automata	I-Application
are	O
precisely	O
the	O
context-sensitive	O
languages	O
.	O
</s>
<s>
First	O
LBA	O
problem	O
:	O
Is	O
NSPACE(O(n )	O
)	O
=	O
DSPACE(O(n )	O
)	O
?	O
</s>
<s>
Savitch	O
's	O
theorem	O
provides	O
an	O
initial	O
insight	O
,	O
that	O
NSPACE(O(n )	O
)	O
⊆	O
DSPACE(O(n2 )	O
)	O
.	O
</s>
