Theoretical and Experimental DNA Computation (Natural ...

64 3 Models of Molecular Computation
putation that proceeds by the execution of a single operation per time step).
In [30], Berry and Boudol describe a machine that may be used by theorists
in the field of concurrent programming. This research is concerned with the
study of machine models that allow multiple processes executing in parallel.
We briefly describe their Chemical Abstract Machine (CHAM) in the next
section, but first describe its origins.
Most concurrency models are based on architectural principles, for example,
networks of processes communicating via “channels” or “threads.” In
[20], Banâtre and Le Métayer argue that the imposition of architectual control
structures in programming languages actually hinders the programmer,
rather than helping him or her. They quote Chandy and Misra [41]:
The basic problem in programming is managing complexity. We cannot
address that problem as long as we lump together concerns about
the core problem to be solved, the language in which the program is
to be written, and the hardware on which the program is to execute.
Program development should begin by focusing attention on the problem
the be solved and postponing considerations of architecture and
language constructs.
Banâtre and Le Métayer argue that it should be possible to construct an abstract,
high-level version of a program to solve a given problem, and that that
should be free from artificial sequentiality due to architectural constraints.
They cite the simple example of finding the maximum element in a nonempty
set [21].
In a “traditional”, imperative language, the code may look like this. Note
that n denotes the size of the set, which is stored in the array set[].
maximum ← set[0]
for loop =1ton − 1 do begin
c ← set[loop]
if c > maximum then maximum ← c
end
In this case the program takes the initial maximum to be the first element,
and then scans the set in a linear fashion. If an element is found that is larger
than the current maximum, then that element becomes the current maximum,
and so on until the end of the set is reached.
The program imposes a total ordering on the comparisons of the elements
when, in fact, the maximum of a set can be computed by performing comparisons
in any order: