<s>
In	O
computer	B-General_Concept
science	I-General_Concept
,	O
the	O
Actor	B-Application
model	I-Application
and	I-Application
process	I-Application
calculi	I-Application
are	O
two	O
closely	O
related	O
approaches	O
to	O
the	O
modelling	O
of	O
concurrent	B-Operating_System
digital	I-Operating_System
computation	I-Operating_System
.	O
</s>
<s>
See	O
Actor	B-Application
model	I-Application
and	I-Application
process	I-Application
calculi	I-Application
history	I-Application
.	O
</s>
<s>
There	O
is	O
only	O
one	O
Actor	B-Application
model	I-Application
(	O
although	O
it	O
has	O
numerous	O
formal	O
systems	O
for	O
design	O
,	O
analysis	O
,	O
verification	O
,	O
modeling	O
,	O
etc	O
.	O
</s>
<s>
)	O
;	O
there	O
are	O
numerous	O
process	O
calculi	O
,	O
developed	O
for	O
reasoning	O
about	O
a	O
variety	O
of	O
different	O
kinds	O
of	O
concurrent	B-Operating_System
systems	I-Operating_System
at	O
various	O
levels	O
of	O
detail	O
(	O
including	O
calculi	O
that	O
incorporate	O
time	O
,	O
stochastic	O
transitions	O
,	O
or	O
constructs	O
specific	O
to	O
application	O
areas	O
such	O
as	O
security	O
analysis	O
)	O
.	O
</s>
<s>
The	O
Actor	B-Application
model	I-Application
was	O
inspired	O
by	O
the	O
laws	O
of	O
physics	O
and	O
depends	O
on	O
them	O
for	O
its	O
fundamental	O
axioms	O
,	O
i.e.	O
</s>
<s>
physical	O
laws	O
(	O
see	O
Actor	B-Application
model	I-Application
theory	O
)	O
;	O
the	O
process	O
calculi	O
were	O
originally	O
inspired	O
by	O
algebra	O
.	O
</s>
<s>
In	O
contrast	O
,	O
actors	O
in	O
the	O
Actor	B-Application
model	I-Application
possess	O
an	O
identity	O
,	O
and	O
communicate	O
by	O
sending	O
messages	O
to	O
the	O
mailing	O
addresses	O
of	O
other	O
actors	O
(	O
this	O
style	O
of	O
communication	O
can	O
also	O
be	O
used	O
to	O
model	O
channel-like	O
communications	O
—	O
see	O
below	O
)	O
.	O
</s>
<s>
The	O
publications	O
on	O
the	O
Actor	B-Application
model	I-Application
and	O
on	O
process	O
calculi	O
have	O
a	O
fair	O
number	O
of	O
cross-references	O
,	O
acknowledgments	O
,	O
and	O
reciprocal	O
citations	O
(	O
see	O
Actor	B-Application
model	I-Application
and	I-Application
process	I-Application
calculi	I-Application
history	I-Application
)	O
.	O
</s>
<s>
Some	O
process	O
calculi	O
differ	O
from	O
the	O
Actor	B-Application
model	I-Application
in	O
their	O
use	O
of	O
channels	O
as	O
opposed	O
to	O
direct	O
communication	O
.	O
</s>
<s>
Each	O
put	O
communication	O
has	O
a	O
message	O
and	O
an	O
address	O
to	O
which	O
an	O
acknowledgment	O
is	O
sent	O
when	O
the	O
message	O
is	O
received	O
by	O
a	O
get	O
communication	O
from	O
the	O
channel	O
in	O
FIFO	B-Operating_System
order	O
.	O
</s>
<s>
Because	O
only	O
one	O
guard	O
can	O
be	O
chosen	O
,	O
a	O
guarded	O
choice	O
command	O
in	O
general	O
effectively	O
requires	O
a	O
kind	O
of	O
two-phase	B-General_Concept
commit	I-General_Concept
protocol	I-General_Concept
or	O
perhaps	O
even	O
a	O
three-phase	O
commit	O
protocol	O
if	O
time-outs	O
are	O
allowed	O
in	O
guards	O
(	O
as	O
in	O
Occam	O
3	O
 [ 1992 ] 	O
)	O
.	O
</s>
<s>
As	O
pointed	O
out	O
in	O
Knabe	O
[1992],	O
a	O
problem	O
with	O
the	O
above	O
protocol	O
(	O
A	O
simple	O
distributed	O
protocol	O
)	O
is	O
that	O
the	O
process	O
Z	O
might	O
never	O
accept	O
the	O
stop	O
message	O
from	O
X	O
(	O
a	O
phenomenon	O
called	O
starvation	B-Operating_System
)	O
and	O
consequently	O
the	O
above	O
program	O
might	O
never	O
print	O
anything	O
.	O
</s>
<s>
By	O
the	O
laws	O
of	O
Actor	O
semantics	O
,	O
the	O
above	O
Actor	B-Application
system	I-Application
will	O
always	O
halt	O
when	O
the	O
Actors	O
X	O
,	O
Y	O
,	O
are	O
Z	O
are	O
each	O
sent	O
a	O
"	O
start	O
"	O
message	O
resulting	O
in	O
sending	O
print	O
a	O
number	O
that	O
can	O
be	O
unbounded	O
large	O
.	O
</s>
<s>
The	O
difference	O
between	O
the	O
CSP	O
program	O
and	O
the	O
Actor	B-Application
system	I-Application
is	O
that	O
the	O
Actor	O
Z	O
does	O
not	O
get	O
messages	O
using	O
a	O
guarded	O
choice	O
command	O
from	O
multiple	O
channels	O
.	O
</s>
<s>
Instead	O
it	O
processes	O
messages	O
in	O
arrival	O
ordering	O
,	O
and	O
by	O
the	O
laws	O
for	O
Actor	B-Application
systems	I-Application
,	O
the	O
stop	O
message	O
is	O
guaranteed	O
to	O
arrive	O
.	O
</s>
<s>
As	O
pointed	O
out	O
in	O
Knabe	O
[1992],	O
an	O
issue	O
with	O
the	O
above	O
protocol	O
(	O
A	O
simple	O
distributed	O
protocol	O
)	O
is	O
that	O
the	O
process	O
Bidder2	O
might	O
never	O
accept	O
a	O
bid	O
from	O
Bid1	O
or	O
Bid2	O
(	O
a	O
phenomenon	O
called	O
livelock	B-Application
)	O
and	O
consequently	O
process2	O
might	O
never	O
be	O
sent	O
anything	O
.	O
</s>
<s>
Indeed	O
,	O
as	O
shown	O
in	O
the	O
previous	O
section	O
(	O
Livelock	B-Application
)	O
,	O
the	O
number	O
of	O
communications	O
can	O
be	O
unbounded	O
.	O
</s>
<s>
Starvation	B-Operating_System
.	O
</s>
<s>
The	O
use	O
of	O
synchronous	O
channels	O
can	O
cause	O
starvation	B-Operating_System
when	O
a	O
process	O
attempts	O
to	O
get	O
messages	O
from	O
multiple	O
channels	O
in	O
a	O
guarded	O
choice	O
command	O
.	O
</s>
<s>
Livelock	B-Application
.	O
</s>
<s>
The	O
use	O
of	O
synchronous	O
channels	O
can	O
cause	O
a	O
process	O
to	O
be	O
caught	O
in	O
livelock	B-Application
when	O
it	O
attempts	O
to	O
get	O
messages	O
from	O
multiple	O
channels	O
in	O
a	O
guarded	O
choice	O
command	O
.	O
</s>
<s>
Subsequently	O
,	O
several	O
different	O
process	O
calculi	O
intended	O
to	O
provide	O
algebraic	O
reasoning	O
about	O
Actor	B-Application
systems	I-Application
have	O
been	O
developed	O
in	O
,	O
,	O
.	O
</s>
<s>
Will	O
Clinger	O
(	O
building	O
on	O
the	O
work	O
of	O
Irene	O
Greif	O
[1975],	O
Gordon	O
Plotkin	O
[1976],	O
Henry	O
Baker	O
[1978],	O
Michael	O
Smyth	O
[1978],	O
and	O
Francez	O
,	O
Hoare	O
,	O
Lehmann	O
,	O
and	O
de	O
Roever	O
 [ 1979 ] 	O
)	O
published	O
the	O
first	O
satisfactory	O
mathematical	O
denotational	B-Application
theory	O
of	O
the	O
Actor	B-Application
model	I-Application
using	O
domain	O
theory	O
in	O
his	O
dissertation	O
in	O
1981	O
.	O
</s>
<s>
His	O
semantics	O
contrasted	O
the	O
unbounded	B-Application
nondeterminism	I-Application
of	O
the	O
Actor	B-Application
model	I-Application
with	O
the	O
bounded	O
nondeterminism	O
of	O
CSP	O
[	O
Hoare	O
1978 ]	O
and	O
Concurrent	O
Processes	O
[	O
Milne	O
and	O
Milner	O
1979 ]	O
(	O
see	O
denotational	B-Application
semantics	I-Application
)	O
.	O
</s>
<s>
Roscoe	O
 [ 2005 ] 	O
has	O
developed	O
a	O
denotational	B-Application
semantics	I-Application
with	O
unbounded	B-Application
nondeterminism	I-Application
for	O
a	O
subsequent	O
version	O
of	O
Communicating	O
Sequential	O
Processes	O
Hoare	O
 [ 1985 ] 	O
.	O
</s>
<s>
More	O
recently	O
Carl	O
Hewitt	O
 [ 2006b ] 	O
developed	O
a	O
denotational	B-Application
semantics	I-Application
for	O
Actors	O
based	O
on	O
timed	O
diagrams	O
.	O
</s>
