<s>
In	O
theoretical	O
computer	O
science	O
and	O
formal	O
language	O
theory	O
,	O
the	O
equivalence	B-General_Concept
problem	I-General_Concept
is	O
the	O
question	O
of	O
determining	O
,	O
given	O
two	O
representations	O
of	O
formal	O
languages	O
,	O
whether	O
they	O
denote	O
the	O
same	O
formal	O
language	O
.	O
</s>
<s>
For	O
instance	O
,	O
in	O
the	O
case	O
of	O
finite-state	B-Architecture
automata	I-Architecture
,	O
equivalence	O
is	O
decidable	O
,	O
and	O
the	O
problem	O
is	O
PSPACE-complete	O
.	O
</s>
<s>
Further	O
,	O
in	O
the	O
case	O
of	O
deterministic	B-Application
pushdown	I-Application
automata	I-Application
,	O
equivalence	O
is	O
decidable	O
,	O
Géraud	O
Sénizergues	O
won	O
the	O
Gödel	O
Prize	O
for	O
this	O
result	O
.	O
</s>
<s>
It	O
becomes	O
an	O
undecidable	O
problem	O
for	O
pushdown	B-Application
automata	I-Application
or	O
any	O
machine	O
that	O
can	O
decide	O
context-free	O
languages	O
or	O
more	O
powerful	O
languages	O
.	O
</s>
