<s>
The	O
intersection	B-Application
non-emptiness	I-Application
problem	I-Application
,	O
also	O
known	O
as	O
finite	O
automaton	O
intersection	O
problem	O
or	O
the	O
non-emptiness	O
of	O
intersection	O
problem	O
,	O
is	O
a	O
PSPACE-complete	O
decision	O
problem	O
from	O
the	O
field	O
of	O
automata	B-Application
theory	I-Application
.	O
</s>
<s>
Non-emptiness	O
problems	O
have	O
been	O
studied	O
in	O
the	O
field	O
of	O
automata	B-Application
theory	I-Application
for	O
many	O
years	O
.	O
</s>
<s>
In	O
particular	O
,	O
the	O
intersection	B-Application
non-emptiness	I-Application
problem	I-Application
is	O
defined	O
as	O
follows	O
.	O
</s>
<s>
There	O
is	O
a	O
common	O
exponential	O
time	O
algorithm	O
that	O
solves	O
the	O
intersection	B-Application
non-emptiness	I-Application
problem	I-Application
based	O
on	O
the	O
Cartesian	O
product	O
construction	O
introduced	O
by	O
Michael	O
O	O
.	O
Rabin	O
and	O
Dana	O
Scott	O
.	O
</s>
<s>
Therefore	O
,	O
a	O
breadth-first	B-Algorithm
search	I-Algorithm
(	O
or	O
depth-first	B-Algorithm
search	I-Algorithm
)	O
within	O
the	O
product	O
automaton	O
's	O
state	O
diagram	O
will	O
determine	O
whether	O
there	O
exists	O
a	O
path	O
from	O
the	O
product	O
start	O
state	O
to	O
one	O
of	O
the	O
product	O
final	O
states	O
.	O
</s>
<s>
The	O
intersection	B-Application
non-emptiness	I-Application
problem	I-Application
was	O
shown	O
to	O
be	O
PSPACE-complete	O
in	O
a	O
work	O
by	O
Dexter	O
Kozen	O
in	O
1977	O
.	O
</s>
