The relationships between a more general class of membrane systems, called kernel P systems, and other variants of membrane systems are presented. The process of translating the main types of spiking P systems into kernel P systems are analysed with respect to certain complexity metrics. Formal verification, through model checking, and testing procedures are discussed for the models obtained from these mappings. Membrane computing is a natural computing paradigm inspired by the structure and bio-chemical interactions of the living cells. The key models are called membrane systems or P systems. A standard (basic) membrane system model consists of three main elements: (i) a set of components, called membranes or regions, organised in a hierarchical structure and included in an outer membrane, called the skin membrane; each region contains (ii) multisets of objects and (iii) evolution and communication rules acting on the local objects, transforming or sending them to the regions from its vicinity. The main membrane-based structure is inspired by the eukaryotic cell's structure containing a nucleus and specialised membrane-bound organelles such as mitochondria, endoplasmic reticulum, Golgi apparatus. The objects encode either simple elements (hydrogen, oxygen, nitrogen, carbon, sulfur) or bio-chemical compounds (carbohydrates, lipids, proteins, and nucleic acids) and the rules stand for various interactions (chemical reactions, more complex transcription and translation, cell division and cell death processes).
https://www.bradford.ac.uk/staff/mgheorghe// (M. Gheorghe)
CEUR Workshop
ISSN1613-0073
the implementations. They are supported by an expressive domain specific formal language allowing
the models to be simulated with a software framework, called kPWorkbench, which also includes a
verification component. A detailed presentation of this tool has been made in [
A class of neural-like P systems, called Spiking Neural P systems (SN P systems, for short), has been
introduced in [
In this work are first presented some relationships between, on the one hand, kP systems and, on the other hand, neural-like P systems and membrane systems with active membranes. The main focus is on describing how the classes of standard and extended SN P systems with and with no delay, with colored spikes, multiple channels, anti-spikes, polarizations, weights on synapses, potential and threshold. are mapped into kP systems exhibiting the same behaviour. Two types of encoding the computation results and various strategies of using the rules that are defined and investigated for SN P systems are studied in the context of kP systems as well. A logical gate example illustrates how diferent SN P systems and their kP system counterparts can model the problem. Finally, a short presentation on how verification and testing methods developed for kP systems can be used to formally verify the SN P system model of the logical gate example and test its implementation.
Algorithms for translating each of the SN P systems investigated into corresponding kP systems are provided and metrics to assess the impact of various features of the classes of SN P systems considered on the complexity of their kP system representations are presented. Moreover, the instrumentation provided by the kPWorkbench environment facilitates the verification of the model correctness, through model checking methods, and the automated testing of the implementations based on the initial SN P systems.
Some future research developments based on the work reported here are: (i) investigate relationships between other classes of SN P systems and kP systems; (ii) extend the set of features of kP systems such that they provide better mappings for the SN P systems, with respect to the complexity metrics introduced; (iii) identify more complex examples or case studies based on SN P systems and apply formal verification and testing procedures to their corresponding kP systems, tracing the results back to the original models.
This work reported here has been partially supported by the Royal Society grant IES\R3\213176, 2022-2025.
The author has not employed any Generative AI tools.