<s>
In	O
computer	B-General_Concept
science	I-General_Concept
,	O
formal	B-Architecture
methods	I-Architecture
are	O
mathematically	O
rigorous	O
techniques	O
for	O
the	O
specification	B-Application
,	O
development	O
,	O
analysis	O
,	O
and	O
verification	O
of	O
software	O
and	O
hardware	B-Architecture
systems	O
.	O
</s>
<s>
The	O
use	O
of	O
formal	B-Architecture
methods	I-Architecture
for	O
software	O
and	O
hardware	B-Architecture
design	O
is	O
motivated	O
by	O
the	O
expectation	O
that	O
,	O
as	O
in	O
other	O
engineering	O
disciplines	O
,	O
performing	O
appropriate	O
mathematical	O
analysis	O
can	O
contribute	O
to	O
the	O
reliability	O
and	O
robustness	O
of	O
a	O
design	O
.	O
</s>
<s>
Formal	B-Architecture
methods	I-Architecture
employ	O
a	O
variety	O
of	O
theoretical	O
computer	B-General_Concept
science	I-General_Concept
fundamentals	O
,	O
including	O
logic	B-Application
calculi	O
,	O
formal	O
languages	O
,	O
automata	B-Application
theory	I-Application
,	O
control	O
theory	O
,	O
program	B-Application
semantics	I-Application
,	O
type	O
systems	O
,	O
and	O
type	O
theory	O
.	O
</s>
<s>
It	O
defers	O
the	O
task	O
of	O
completing	O
the	O
semantics	B-Application
to	O
a	O
later	O
stage	O
,	O
which	O
is	O
then	O
done	O
either	O
by	O
human	O
interpretation	O
or	O
by	O
interpretation	O
through	O
software	O
like	O
code	O
or	O
test	O
case	O
generators	O
.	O
</s>
<s>
Formal	B-Architecture
methods	I-Architecture
can	O
be	O
used	O
at	O
a	O
number	O
of	O
levels	O
:	O
</s>
<s>
Level	O
0	O
:	O
Formal	B-Application
specification	I-Application
may	O
be	O
undertaken	O
and	O
then	O
a	O
program	O
developed	O
from	O
this	O
informally	O
.	O
</s>
<s>
This	O
has	O
been	O
dubbed	O
formal	B-Architecture
methods	I-Architecture
lite	O
.	O
</s>
<s>
For	O
example	O
,	O
proofs	O
of	O
properties	O
or	O
refinement	O
from	O
the	O
specification	B-Application
to	O
a	O
program	O
may	O
be	O
undertaken	O
.	O
</s>
<s>
As	O
with	O
programming	B-Application
language	I-Application
semantics	I-Application
,	O
styles	O
of	O
formal	B-Architecture
methods	I-Architecture
may	O
be	O
roughly	O
classified	O
as	O
follows	O
:	O
</s>
<s>
Denotational	B-Application
semantics	I-Application
,	O
in	O
which	O
the	O
meaning	O
of	O
a	O
system	O
is	O
expressed	O
in	O
the	O
mathematical	O
theory	O
of	O
domains	O
.	O
</s>
<s>
Operational	O
semantics	B-Application
,	O
in	O
which	O
the	O
meaning	O
of	O
a	O
system	O
is	O
expressed	O
as	O
a	O
sequence	O
of	O
actions	O
of	O
a	O
(	O
presumably	O
)	O
simpler	O
computational	O
model	O
.	O
</s>
<s>
Proponents	O
of	O
such	O
methods	O
point	O
to	O
the	O
simplicity	O
of	O
their	O
models	O
as	O
a	O
means	O
to	O
expressive	O
clarity	O
;	O
critics	O
counter	O
that	O
the	O
problem	O
of	O
semantics	B-Application
has	O
just	O
been	O
delayed	O
(	O
who	O
defines	O
the	O
semantics	B-Application
of	O
the	O
simpler	O
model	O
?	O
</s>
<s>
Axiomatic	O
semantics	B-Application
,	O
in	O
which	O
the	O
meaning	O
of	O
the	O
system	O
is	O
expressed	O
in	O
terms	O
of	O
preconditions	O
and	O
postconditions	O
which	O
are	O
true	O
before	O
and	O
after	O
the	O
system	O
performs	O
a	O
task	O
,	O
respectively	O
.	O
</s>
<s>
Proponents	O
note	O
the	O
connection	O
to	O
classical	O
logic	B-Application
;	O
critics	O
note	O
that	O
such	O
semantics	B-Application
never	O
really	O
describe	O
what	O
a	O
system	O
does	O
(	O
merely	O
what	O
is	O
true	O
before	O
and	O
afterwards	O
)	O
.	O
</s>
<s>
Some	O
practitioners	O
believe	O
that	O
the	O
formal	B-Architecture
methods	I-Architecture
community	O
has	O
overemphasized	O
full	O
formalization	O
of	O
a	O
specification	B-Application
or	O
design	O
.	O
</s>
<s>
As	O
an	O
alternative	O
,	O
various	O
lightweight	O
formal	B-Architecture
methods	I-Architecture
,	O
which	O
emphasize	O
partial	O
specification	B-Application
and	O
focused	O
application	O
,	O
have	O
been	O
proposed	O
.	O
</s>
<s>
Examples	O
of	O
this	O
lightweight	O
approach	O
to	O
formal	B-Architecture
methods	I-Architecture
include	O
the	O
Alloy	B-Application
object	O
modelling	O
notation	O
,	O
Denney	O
's	O
synthesis	O
of	O
some	O
aspects	O
of	O
the	O
Z	B-Language
notation	I-Language
with	O
use	B-Architecture
case	I-Architecture
driven	O
development	O
,	O
and	O
the	O
CSK	O
VDM	B-Application
Tools	O
.	O
</s>
<s>
Formal	B-Architecture
methods	I-Architecture
can	O
be	O
applied	O
at	O
various	O
points	O
through	O
the	O
development	O
process	O
.	O
</s>
<s>
Formal	B-Architecture
methods	I-Architecture
may	O
be	O
used	O
to	O
give	O
a	O
description	O
of	O
the	O
system	O
to	O
be	O
developed	O
,	O
at	O
whatever	O
level(s )	O
of	O
detail	O
desired	O
.	O
</s>
<s>
This	O
formal	O
description	O
can	O
be	O
used	O
to	O
guide	O
further	O
development	O
activities	O
(	O
see	O
following	O
sections	O
)	O
;	O
additionally	O
,	O
it	O
can	O
be	O
used	O
to	O
verify	O
that	O
the	O
requirements	O
for	O
the	O
system	O
being	O
developed	O
have	O
been	O
completely	O
and	O
accurately	O
specified	O
,	O
or	O
formalising	O
system	O
requirements	O
by	O
expressing	O
them	O
in	O
a	O
formal	O
language	O
with	O
a	O
precise	O
and	O
unambiguously	O
defined	O
syntax	O
and	O
semantics	B-Application
.	O
</s>
<s>
The	O
need	O
for	O
formal	B-Application
specification	I-Application
systems	O
has	O
been	O
noted	O
for	O
years	O
.	O
</s>
<s>
In	O
the	O
ALGOL	B-Language
58	I-Language
report	O
,	O
John	O
Backus	O
presented	O
a	O
formal	O
notation	O
for	O
describing	O
programming	O
language	O
syntax	O
,	O
later	O
named	O
Backus	O
normal	O
form	O
then	O
renamed	O
Backus	O
–	O
Naur	O
form	O
(	O
BNF	O
)	O
.	O
</s>
<s>
"	O
Therefore	O
the	O
formal	O
treatment	O
of	O
the	O
semantics	B-Application
of	O
legal	O
programs	O
will	O
be	O
included	O
in	O
a	O
subsequent	O
paper.	O
"	O
</s>
<s>
Formal	O
development	O
is	O
the	O
use	O
of	O
formal	B-Architecture
methods	I-Architecture
as	O
an	O
integrated	O
part	O
of	O
a	O
tool-supported	O
system	O
development	O
process	O
.	O
</s>
<s>
Once	O
a	O
formal	B-Application
specification	I-Application
has	O
been	O
produced	O
,	O
the	O
specification	B-Application
may	O
be	O
used	O
as	O
a	O
guide	O
while	O
the	O
concrete	O
system	O
is	O
developed	O
during	O
the	O
design	O
process	O
(	O
i.e.	O
,	O
realized	O
typically	O
in	O
software	O
,	O
but	O
also	O
potentially	O
in	O
hardware	B-Architecture
)	O
.	O
</s>
<s>
If	O
the	O
formal	B-Application
specification	I-Application
is	O
in	O
operational	O
semantics	B-Application
,	O
the	O
observed	O
behavior	O
of	O
the	O
concrete	O
system	O
can	O
be	O
compared	O
with	O
the	O
behavior	O
of	O
the	O
specification	B-Application
(	O
which	O
itself	O
should	O
be	O
executable	O
or	O
simulatable	O
)	O
.	O
</s>
<s>
Additionally	O
,	O
the	O
operational	O
commands	O
of	O
the	O
specification	B-Application
may	O
be	O
amenable	O
to	O
direct	O
translation	O
into	O
executable	O
code	O
.	O
</s>
<s>
If	O
the	O
formal	B-Application
specification	I-Application
is	O
in	O
axiomatic	O
semantics	B-Application
,	O
the	O
preconditions	O
and	O
postconditions	O
of	O
the	O
specification	B-Application
may	O
become	O
assertions	O
in	O
the	O
executable	O
code	O
.	O
</s>
<s>
Formal	O
verification	O
is	O
the	O
use	O
of	O
software	O
tools	O
to	O
prove	O
properties	O
of	O
a	O
formal	B-Application
specification	I-Application
,	O
or	O
to	O
prove	O
that	O
a	O
formal	O
model	O
of	O
a	O
system	O
implementation	O
satisfies	O
its	O
specification	B-Application
.	O
</s>
<s>
Once	O
a	O
formal	B-Application
specification	I-Application
has	O
been	O
developed	O
,	O
the	O
specification	B-Application
may	O
be	O
used	O
as	O
the	O
basis	O
for	O
proving	O
properties	O
of	O
the	O
specification	B-Application
,	O
and	O
by	O
inference	O
,	O
properties	O
of	O
the	O
system	O
implementation	O
.	O
</s>
<s>
Automated	B-Application
theorem	I-Application
proving	I-Application
,	O
in	O
which	O
a	O
system	O
attempts	O
to	O
produce	O
a	O
formal	O
proof	O
from	O
scratch	O
,	O
given	O
a	O
description	O
of	O
the	O
system	O
,	O
a	O
set	O
of	O
logical	O
axioms	O
,	O
and	O
a	O
set	O
of	O
inference	O
rules	O
.	O
</s>
<s>
Model	B-Application
checking	I-Application
,	O
in	O
which	O
a	O
system	O
verifies	O
certain	O
properties	O
by	O
means	O
of	O
an	O
exhaustive	O
search	O
of	O
all	O
possible	O
states	O
that	O
a	O
system	O
could	O
enter	O
during	O
its	O
execution	O
.	O
</s>
<s>
Some	O
automated	B-Application
theorem	I-Application
provers	I-Application
require	O
guidance	O
as	O
to	O
which	O
properties	O
are	O
"	O
interesting	O
"	O
enough	O
to	O
pursue	O
,	O
while	O
others	O
work	O
without	O
human	O
intervention	O
.	O
</s>
<s>
Model	B-Application
checkers	I-Application
can	O
quickly	O
get	O
bogged	O
down	O
in	O
checking	O
millions	O
of	O
uninteresting	O
states	O
if	O
not	O
given	O
a	O
sufficiently	O
abstract	O
model	O
.	O
</s>
<s>
Some	O
modern	O
model	B-Application
checking	I-Application
tools	O
produce	O
a	O
"	O
proof	O
log	O
"	O
detailing	O
each	O
step	O
in	O
their	O
proof	O
,	O
making	O
it	O
possible	O
to	O
perform	O
,	O
given	O
suitable	O
tools	O
,	O
independent	O
verification	O
.	O
</s>
<s>
Formal	B-Architecture
methods	I-Architecture
are	O
applied	O
in	O
different	O
areas	O
of	O
hardware	B-Architecture
and	O
software	O
,	O
including	O
routers	O
,	O
Ethernet	O
switches	O
,	O
routing	O
protocols	O
,	O
security	O
applications	O
,	O
and	O
operating	O
system	O
microkernels	O
such	O
as	O
seL4	O
.	O
</s>
<s>
There	O
are	O
several	O
examples	O
in	O
which	O
they	O
have	O
been	O
used	O
to	O
verify	O
the	O
functionality	O
of	O
the	O
hardware	B-Architecture
and	O
software	O
used	O
in	O
DCs	O
.	O
</s>
<s>
IBM	O
used	O
ACL2	B-Application
,	O
a	O
theorem	B-Application
prover	I-Application
,	O
in	O
the	O
AMD	O
x86	O
processor	O
development	O
process	O
.	O
</s>
<s>
Intel	O
uses	O
such	O
methods	O
to	O
verify	O
its	O
hardware	B-Architecture
and	O
firmware	O
(	O
permanent	O
software	O
programmed	O
into	O
a	O
read-only	O
memory	O
)	O
.	O
</s>
<s>
Dansk	O
Datamatik	O
Center	O
used	O
formal	B-Architecture
methods	I-Architecture
in	O
the	O
1980s	O
to	O
develop	O
a	O
compiler	O
system	O
for	O
the	O
Ada	B-Language
programming	I-Language
language	I-Language
that	O
went	O
on	O
to	O
become	O
a	O
long-lived	O
commercial	O
product	O
.	O
</s>
<s>
There	O
are	O
several	O
other	O
projects	O
of	O
NASA	O
in	O
which	O
formal	B-Architecture
methods	I-Architecture
are	O
applied	O
,	O
such	O
as	O
Next	O
Generation	O
Air	O
Transportation	O
System	O
,	O
Unmanned	O
Aircraft	O
System	O
integration	O
in	O
National	O
Airspace	O
System	O
,	O
and	O
Airborne	O
Coordinated	O
Conflict	O
Resolution	O
and	O
Detection	O
(	O
ACCoRD	O
)	O
.	O
</s>
<s>
B-Method	B-Application
with	O
Atelier	B-Application
B	I-Application
,	O
is	O
used	O
to	O
develop	O
safety	O
automatisms	O
for	O
the	O
various	O
subways	O
installed	O
throughout	O
the	O
world	O
by	O
Alstom	O
and	O
Siemens	O
,	O
and	O
also	O
for	O
Common	O
Criteria	O
certification	O
and	O
the	O
development	O
of	O
system	O
models	O
by	O
ATMEL	O
and	O
STMicroelectronics	O
.	O
</s>
<s>
Formal	O
verification	O
has	O
been	O
frequently	O
used	O
in	O
hardware	B-Architecture
by	O
most	O
of	O
the	O
well-known	O
hardware	B-Architecture
vendors	O
,	O
such	O
as	O
IBM	O
,	O
Intel	O
,	O
and	O
AMD	O
.	O
</s>
<s>
There	O
are	O
many	O
areas	O
of	O
hardware	B-Architecture
,	O
where	O
Intel	O
have	O
used	O
FMs	O
to	O
verify	O
the	O
working	O
of	O
the	O
products	O
,	O
such	O
as	O
parameterized	O
verification	O
of	O
cache-coherent	O
protocol	O
,	O
Intel	O
Core	O
i7	O
processor	O
execution	O
engine	O
validation	O
(	O
using	O
theorem	B-Application
proving	I-Application
,	O
BDDs	B-Application
,	O
and	O
symbolic	O
evaluation	O
)	O
,	O
optimization	O
for	O
Intel	O
IA-64	O
architecture	O
using	O
HOL	O
light	O
theorem	B-Application
prover	I-Application
,	O
and	O
verification	O
of	O
high-performance	O
dual-port	O
gigabit	O
Ethernet	O
controller	O
with	O
support	O
for	O
PCI	O
express	O
protocol	O
and	O
Intel	O
advance	O
management	O
technology	O
using	O
Cadence	O
.	O
</s>
<s>
Similarly	O
,	O
IBM	O
has	O
used	O
formal	B-Architecture
methods	I-Architecture
in	O
the	O
verification	O
of	O
power	O
gates	O
,	O
registers	O
,	O
and	O
functional	O
verification	O
of	O
the	O
IBM	O
Power7	O
microprocessor	O
.	O
</s>
<s>
In	O
software	O
development	O
,	O
formal	B-Architecture
methods	I-Architecture
are	O
mathematical	O
approaches	O
to	O
solving	O
software	O
(	O
and	O
hardware	B-Architecture
)	O
problems	O
at	O
the	O
requirements	O
,	O
specification	B-Application
,	O
and	O
design	O
levels	O
.	O
</s>
<s>
Formal	B-Architecture
methods	I-Architecture
are	O
most	O
likely	O
to	O
be	O
applied	O
to	O
safety-critical	O
or	O
security-critical	O
software	O
and	O
systems	O
,	O
such	O
as	O
avionics	B-Application
software	I-Application
.	O
</s>
<s>
Software	O
safety	O
assurance	O
standards	O
,	O
such	O
as	O
DO-178C	O
allows	O
the	O
usage	O
of	O
formal	B-Architecture
methods	I-Architecture
through	O
supplementation	O
,	O
and	O
Common	O
Criteria	O
mandates	O
formal	B-Architecture
methods	I-Architecture
at	O
the	O
highest	O
levels	O
of	O
categorization	O
.	O
</s>
<s>
For	O
sequential	O
software	O
,	O
examples	O
of	O
formal	B-Architecture
methods	I-Architecture
include	O
the	O
B-Method	B-Application
,	O
the	O
specification	B-Application
languages	I-Application
used	O
in	O
automated	B-Application
theorem	I-Application
proving	I-Application
,	O
RAISE	B-Application
,	O
and	O
the	O
Z	B-Language
notation	I-Language
.	O
</s>
<s>
In	O
functional	B-Language
programming	I-Language
,	O
property-based	B-Application
testing	I-Application
has	O
allowed	O
the	O
mathematical	O
specification	B-Application
and	O
testing	O
(	O
if	O
not	O
exhaustive	O
testing	O
)	O
of	O
the	O
expected	O
behaviour	O
of	O
individual	O
functions	O
.	O
</s>
<s>
The	O
Object	B-Language
Constraint	I-Language
Language	I-Language
(	O
and	O
specializations	O
such	O
as	O
Java	B-Language
Modeling	I-Language
Language	I-Language
)	O
has	O
allowed	O
object-oriented	O
systems	O
to	O
be	O
formally	O
specified	O
,	O
if	O
not	O
necessarily	O
formally	O
verified	O
.	O
</s>
<s>
For	O
concurrent	O
software	O
and	O
systems	O
,	O
Petri	B-Operating_System
nets	I-Operating_System
,	O
process	O
algebra	O
,	O
and	O
finite	B-Architecture
state	I-Architecture
machines	I-Architecture
(	O
which	O
are	O
based	O
on	O
automata	B-Application
theory	I-Application
-	O
see	O
also	O
virtual	B-Application
finite	I-Application
state	I-Application
machine	I-Application
or	O
event	B-Application
driven	I-Application
finite	I-Application
state	I-Application
machine	I-Application
)	O
allow	O
executable	O
software	B-Application
specification	I-Application
and	O
can	O
be	O
used	O
to	O
build	O
up	O
and	O
validate	O
application	O
behaviour	O
.	O
</s>
<s>
Another	O
approach	O
to	O
formal	B-Architecture
methods	I-Architecture
in	O
software	O
development	O
is	O
to	O
write	O
a	O
specification	B-Application
in	O
some	O
form	O
of	O
logic	B-Application
—	O
usually	O
a	O
variation	O
of	O
first-order	O
logic	B-Application
(	O
FOL	O
)	O
—	O
and	O
then	O
to	O
directly	O
execute	O
the	O
logic	B-Application
as	O
though	O
it	O
were	O
a	O
program	O
.	O
</s>
<s>
The	O
OWL	B-Language
language	O
,	O
based	O
on	O
Description	B-Language
Logic	I-Language
(	O
DL	O
)	O
,	O
is	O
an	O
example	O
.	O
</s>
<s>
There	O
is	O
also	O
work	O
on	O
mapping	O
some	O
version	O
of	O
English	O
(	O
or	O
another	O
natural	O
language	O
)	O
automatically	O
to	O
and	O
from	O
logic	B-Application
,	O
as	O
well	O
as	O
executing	O
the	O
logic	B-Application
directly	O
.	O
</s>
<s>
Examples	O
are	O
Attempto	B-General_Concept
Controlled	I-General_Concept
English	I-General_Concept
,	O
and	O
Internet	O
Business	O
Logic	B-Application
,	O
which	O
do	O
not	O
seek	O
to	O
control	O
the	O
vocabulary	O
or	O
syntax	O
.	O
</s>
<s>
A	O
feature	O
of	O
systems	O
that	O
support	O
bidirectional	O
English-logic	O
mapping	O
and	O
direct	O
execution	O
of	O
the	O
logic	B-Application
is	O
that	O
they	O
can	O
be	O
made	O
to	O
explain	O
their	O
results	O
,	O
in	O
English	O
,	O
at	O
the	O
business	O
or	O
scientific	O
level	O
.	O
</s>
<s>
There	O
are	O
a	O
variety	O
of	O
formal	B-Architecture
methods	I-Architecture
and	O
notations	O
available	O
.	O
</s>
