Languages generated by numerical P systems with thresholds

Abstract

Numerical P systems with thresholds (NPT systems) are a type of distributive and parallel computing model in the framework of membrane computing, inspired by the mechanism of information processing in cells. In membrane computing, the study of language generating/accepting power of a computing model is essential for understanding its capabilities and limitations, while the language generating/accepting power of NPT systems remains open. In this work, a language hierarchy for NPT systems is established by considering polynomials of degree one as production functions. Specifically, if each production function is a variable with a positive integer coefficient, the NPT systems characterize regular languages. If each production function is a variable with an integer coefficient, the languages generated by the NPT systems are no more than context-sensitive. Further, the NPT systems generate all recursively enumerable languages if each production function is a linear combination of no more than two variables and each term of a production function is a variable with an integer coefficient. The results show that the language generating power of NPT systems is closely related to the number of variables and the range of coefficients in production functions.