<s>
Murφ	B-Language
(	O
/ˈmɝ.fi/	O
,	O
also	O
spelled	O
Murphi	B-Language
)	O
is	O
an	O
explicit-state	O
model	B-Application
checker	I-Application
developed	O
at	O
Stanford	O
University	O
,	O
and	O
widely	O
used	O
for	O
formal	O
verification	O
of	O
cache-coherence	B-General_Concept
protocols	O
.	O
</s>
<s>
Murφ	B-Language
's	O
early	O
history	O
is	O
described	O
in	O
a	O
paper	O
by	O
David	O
Dill	O
.	O
</s>
<s>
The	O
first	O
version	O
of	O
Murφ	B-Language
was	O
designed	O
at	O
Stanford	O
University	O
in	O
1990	O
and	O
1991	O
by	O
Prof	O
.	O
David	O
Dill	O
and	O
his	O
graduate	O
students	O
Andreas	O
Drexler	O
,	O
Alan	O
Hu	O
,	O
and	O
Han	O
Yang	O
,	O
and	O
primarily	O
implemented	O
by	O
Andreas	O
Drexler	O
.	O
</s>
<s>
Ulrich	O
Stern	O
implemented	O
hash	O
compaction	O
,	O
improved	O
the	O
use	O
of	O
disk	O
,	O
and	O
implemented	O
Parallel	O
Murφ	B-Language
.	O
</s>
<s>
Many	O
derivative	O
versions	O
of	O
Murφ	B-Language
have	O
been	O
created	O
since	O
then	O
by	O
other	O
groups	O
.	O
</s>
<s>
The	O
Murφ	B-Language
compiler	O
accepts	O
a	O
model	O
written	O
in	O
the	O
Murφ	B-Language
specification	O
language	O
and	O
outputs	O
C++	B-Language
code	I-Language
that	O
constitutes	O
a	O
verifier	O
for	O
that	O
model	O
.	O
</s>
<s>
(	O
That	O
is	O
,	O
the	O
C++	B-Language
code	I-Language
,	O
when	O
executed	O
,	O
performs	O
explicit-state	O
model	B-Application
checking	I-Application
on	O
the	O
design	O
described	O
by	O
the	O
specification	O
.	O
)	O
</s>
<s>
properties	O
,	O
though	O
Murφ	B-Language
release	O
2.7L	O
did	O
support	O
verification	O
of	O
a	O
set	O
of	O
common	O
LTL	O
liveness	O
properties	O
.	O
</s>
<s>
Murφ	B-Language
was	O
originally	O
applied	O
to	O
verifying	O
cache-coherence	B-General_Concept
protocols	O
,	O
but	O
has	O
been	O
applied	O
to	O
other	O
problems	O
as	O
well	O
,	O
including	O
.	O
</s>
<s>
The	O
Murφ	B-Language
license	O
is	O
similar	O
to	O
the	O
MIT	O
license	O
.	O
</s>
<s>
Murφ	B-Language
may	O
be	O
used	O
,	O
copied	O
,	O
modified	O
,	O
sold	O
,	O
and	O
redistributed	O
for	O
any	O
purpose	O
,	O
provided	O
the	O
copyright	O
notice	O
and	O
license	O
are	O
included	O
,	O
the	O
name	O
of	O
Stanford	O
University	O
is	O
not	O
used	O
for	O
advertising	O
or	O
publicity	O
without	O
permission	O
,	O
and	O
modified	O
versions	O
are	O
not	O
called	O
Murphi	B-Language
without	O
permission	O
.	O
</s>
<s>
Many	O
derivative	O
versions	O
of	O
Murφ	B-Language
have	O
been	O
created	O
,	O
at	O
Stanford	O
and	O
elsewhere	O
,	O
including	O
these	O
:	O
</s>
