Affiliations: Department of Computer Science, The University of
Sheffield, Regent Court, Portobello Street, Sheffield S1 4DP, UK.
f.bernardini@dcs.shef.ac; m.gheorghe@dcs.shef.ac | Department of Computer Science, University of Verona,
strada Le Grazie 15, 37134 Verona, Italy. vincenzo.manca@univr.it
Note: [] Address for correspondence: Department of Computer Science, The
University of Sheffield, Regent Court, Portobello Street, Sheffield S1 4DP,
UK
Abstract: The study of P systems as a mathematical model for biological
systems is an important research topic in the area of membrane computing. In
this respect, the detection of periodicity and almost periodicity as aspects of
the system dynamics seems to be of particular relevance for understanding many
biological processes and their related phenomena. This paper introduces
specific notions of periodicity and almost periodicity for (infinite) sequences
of multisets, which are used to describe the dynamics of P systems.
Specifically, a variant of P systems, called P systems with resources, is
considered where the rules always consume a certain amount of resources, which
are provided in the form of a periodic input sequence of multisets. It is then
shown that P systems with resources are computationally complete (when halting
computations are considered) and that, in general, they can generate sequences
of multisets that are not even almost periodic (once the constraint of having
halting computation is released). However, if P systems with resources are
restricted to be deterministic, it is shown that a characterization of the
behaviour of a particular class of P systems with resources can be obtained in
terms of almost periodicty.
Keywords: Membrane computing, P system, periodicity, almost periodicity, biological model
