  The main purpose of this paper is to study the NP-complete subset-sum
problem, not in the usual context of time-complexity-based classification of
the algorithms (exponential/polynomial), but through a new kind of algorithmic
classification which we introduce based on a property that all known
exponential-time algorithms share. We then construct a theoretical mathematical
environment within which we compare the two classes that are produced from the
new classification; one class is characterized by a normal mathematical nature,
whereas the other by a problematic one. These results are transferred to
exponential/polynomial algorithms, through a conjecture that links the two
classifications. As for the mathematical environment, it consists of a simple
random experiment designed in such a way that the algorithmic operation is
linked to it. We study the random experiment with a stochastic process which is
the main tool for the comparison of the two classes.
