<s>
Formal	B-Application
equivalence	I-Application
checking	I-Application
process	O
is	O
a	O
part	O
of	O
electronic	O
design	O
automation	O
(	O
EDA	O
)	O
,	O
commonly	O
used	O
during	O
the	O
development	O
of	O
digital	O
integrated	O
circuits	O
,	O
to	O
formally	O
prove	O
that	O
two	O
representations	O
of	O
a	O
circuit	O
design	O
exhibit	O
exactly	O
the	O
same	O
behavior	O
.	O
</s>
<s>
The	O
most	O
common	O
approach	O
is	O
to	O
consider	O
the	O
problem	O
of	O
machine	O
equivalence	O
which	O
defines	O
two	O
synchronous	B-Application
design	I-Application
specifications	O
functionally	O
equivalent	O
if	O
,	O
clock	O
by	O
clock	O
,	O
they	O
produce	O
exactly	O
the	O
same	O
sequence	O
of	O
output	O
signals	O
for	O
any	O
valid	O
sequence	O
of	O
input	O
signals	O
.	O
</s>
<s>
Microprocessor	B-Architecture
designers	O
use	O
equivalence	B-Application
checking	I-Application
to	O
compare	O
the	O
functions	O
specified	O
for	O
the	O
instruction	B-General_Concept
set	I-General_Concept
architecture	I-General_Concept
(	O
ISA	O
)	O
with	O
a	O
register	O
transfer	O
level	O
(	O
RTL	O
)	O
implementation	O
,	O
ensuring	O
that	O
any	O
program	O
executed	O
on	O
both	O
models	O
will	O
cause	O
an	O
identical	O
update	O
of	O
the	O
main	O
memory	O
content	O
.	O
</s>
<s>
A	O
system	O
design	O
flow	O
requires	O
comparison	O
between	O
a	O
transaction	O
level	O
model	O
(	O
TLM	O
)	O
,	O
e.g.	O
,	O
written	O
in	O
SystemC	B-Language
and	O
its	O
corresponding	O
RTL	O
specification	O
.	O
</s>
<s>
The	O
register	O
transfer	O
level	O
(	O
RTL	O
)	O
behavior	O
of	O
a	O
digital	O
chip	O
is	O
usually	O
described	O
with	O
a	O
hardware	O
description	O
language	O
,	O
such	O
as	O
Verilog	B-Language
or	O
VHDL	B-Language
.	O
</s>
<s>
This	O
process	O
is	O
called	O
formal	B-Application
equivalence	I-Application
checking	I-Application
and	O
is	O
a	O
problem	O
that	O
is	O
studied	O
under	O
the	O
broader	O
area	O
of	O
formal	O
verification	O
.	O
</s>
<s>
Typically	O
,	O
a	O
formal	B-Application
equivalence	I-Application
checking	I-Application
tool	O
will	O
also	O
indicate	O
with	O
great	O
precision	O
at	O
which	O
point	O
there	O
exists	O
a	O
difference	O
between	O
two	O
representations	O
.	O
</s>
<s>
There	O
are	O
two	O
basic	O
technologies	O
used	O
for	O
boolean	O
reasoning	O
in	O
equivalence	B-Application
checking	I-Application
programs	O
:	O
</s>
<s>
Binary	B-Application
decision	I-Application
diagrams	I-Application
,	O
or	O
BDDs	O
:	O
A	O
specialized	O
data	O
structure	O
designed	O
to	O
support	O
reasoning	O
about	O
boolean	O
functions	O
.	O
</s>
<s>
Conjunctive	O
Normal	O
Form	O
Satisfiability	O
:	O
SAT	B-Algorithm
solvers	O
returns	O
an	O
assignment	O
to	O
the	O
variables	O
of	O
a	O
propositional	O
formula	O
that	O
satisfies	O
it	O
if	O
such	O
an	O
assignment	O
exists	O
.	O
</s>
<s>
Almost	O
any	O
boolean	O
reasoning	O
problem	O
can	O
be	O
expressed	O
as	O
a	O
SAT	B-Algorithm
problem	I-Algorithm
.	O
</s>
<s>
Major	O
products	O
in	O
the	O
Logic	B-Application
Equivalence	I-Application
Checking	I-Application
(	O
LEC	O
)	O
area	O
of	O
EDA	O
are	O
:	O
</s>
<s>
Equivalence	B-Application
Checking	I-Application
of	O
Retimed	O
Circuits	O
:	O
Sometimes	O
it	O
is	O
helpful	O
to	O
move	O
logic	O
from	O
one	O
side	O
of	O
a	O
register	O
to	O
another	O
,	O
and	O
this	O
complicates	O
the	O
checking	O
problem	O
.	O
</s>
<s>
Sequential	O
Equivalence	B-Application
Checking	I-Application
:	O
Sometimes	O
,	O
two	O
machines	O
are	O
completely	O
different	O
at	O
the	O
combinational	O
level	O
,	O
but	O
should	O
give	O
the	O
same	O
outputs	O
if	O
given	O
the	O
same	O
inputs	O
.	O
</s>
<s>
This	O
problem	O
is	O
even	O
harder	O
than	O
sequential	O
equivalence	B-Application
checking	I-Application
,	O
since	O
the	O
outputs	O
of	O
the	O
two	O
programs	O
may	O
appear	O
at	O
different	O
times	O
;	O
but	O
it	O
is	O
possible	O
,	O
and	O
researchers	O
are	O
working	O
on	O
it	O
.	O
</s>
