Biomedical Engineering Reference
In-Depth Information
communication may be possible, that actual communication that will be realized
is unknown in advance and the behavior is non-deterministic. Two processes P and
Q can also be composed in
parallel
by the PAR operator
j
. In this case, both are
concurrently active and can act either independently or with each other.
Finally, the use of a certain channel name may be restricted to a particular
process P by the
new
operator often indicates also as . The concept of scope
of a process prefix abstracts the physical structure of two intersecting molecular
domains and/or of a molecular complex: global channel names and co-names
represent complementary molecular domains and newly declared private channels
define complexes.
Thus, in the syntax of the calculus a process P is written as follows
P
WWD
0
j
X
j
.; r/:P
j
.x/P
j
Œx
D
yP
j
P
j
P
j
P
C
P
j
A.y
1
;:::;y
n
/
where A.y
1
;:::;y
n
/ is the definition of constants (hereafter, y denotes y
1
;:::;y
n
).
Each agent identifier A has a unique defining equation of the form A.y
1
;:::;y
n
/
D
P ,wherethey
i
are distinct and
fn
.P /
f
y
1
;:::;y
n
g
(see below for the definition
of free names
fn
).
The parameter r is the single parameter of an exponential distribution that
characterize the stochastic behavior of the activity corresponding to the prefix .
The replacement of the prefix P of the original semantics of -calculus with
the stochastic variant .; r/:P is the main modification needed to make -calculus
suitable to a realistic simulation of a chemical reaction. The other modifications
concern an extension of the definition
structural congruence
and the definition of
the
race conditions
, governing the dynamic behavior of the system.
The
structural congruence
on processes is defined as the least congruence
satisfying the following clauses:
•
P and Q˛-equivalent (they only differ in the choice of bound names) implies
P
Q,
•
.
P
=
;
C
;
0
/ is a commutative monoid,
•
.
P
=
;
j
;
0
/ is a commutative monoid,
•
.x/.y/P
.y/.x/P; .x/.R
j
S/
.x/R
j
S if x
62
fn
.S /,
.x/.R
j
S/
R
j
.x/S if x
62
fn
.R/,and.x/P
P if x
62
fn
.P /.
•
A. y/
P
f
y=x
g
,ifA. x/
WWD
P is the unique defining equation of constant A.
We recall the notion of free names
fn
./, bound names bn./, and names
n./
D
fn
./
[
bn./ of a label .
Kind
fn
./
bn./
Silent
;
;
xy
Output
f
x; y
g;
x.y/
Input
f
x
g
f
y
g
The dynamic behavior of a process is driven by a race condition. All activities
enabled attempt tp proceed, but only the fastest one succeeds. The fastest activity