Non-Discrete P Systems

Until now, the usual variants of P systems have only a finite number of options in every step of their computations (that is, an associated computation tree is defined for them). In this way, irrespectively whether they are non-deterministic or probabilistic P systems, we obtain a discrete space of computations where the system evolves. Here we present a variant of P systems which in every step can evolve in a non-discrete number of choices. For that, we do not use discrete multisets, but multisets where the multiplicity of the objects can be real (positive) numbers. The inspiration of this paper is that, in vitro, we can control neither the application of the rules nor the exact number of objects, but we deal with an approximate and non natural number of applications (possibly, related with the concentration of the objects in the membrane). In this way, the multiplicity of an object does not reflect the exact number of identical copies of it in the membrane, but its concentration in the solution.