Numerical P systems with production thresholds

Numerical P systems (for short, NP systems) are distributed and parallel computing models inspired both from the structure of living cells and from the economic reality, where the values of variables evolve by programs that are composed by production functions and repartition protocols: the value of a production function is distributed to variables according to the corresponding repartition protocol. In this work, we introduce a new method of using evolution programs into NP systems, where thresholds are associated with production functions. The computation power of NP systems with production thresholds is investigated. Specifically, we prove that NP systems with lower-thresholds (the production function value can be distributed only when it is not smaller than a given constant), with one membrane working both in the all-parallel mode and in the sequential mode, are universal. The universal results of NP systems with lower-thresholds are extended to NP systems with upper-thresholds (the production function value can be distributed only when it is not greater than a given constant) by simulating the former with the latter. These universality results show that NP systems with production thresholds have the potential to implement any computer program or robot behavior.