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
 
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