Numerical P Systems with Thresholds

Numerical P systems are a class of P systems inspired both from the structure of living cells and from economics. In this work, a control of using evolution programs is introduced into numerical P systems: a threshold is considered and a program can be applied only when the values of the variables involved in the production function of the program are greater than/equal to (lower-threshold) or smaller than/equal to (upper-threshold) the threshold. The computational power of numerical P systems with lower-threshold or upper-threshold is investigated. It is proved that numerical P systems with a lower-threshold, with one membrane and linear production functions, working both in the all-parallel mode and in the one-parallel mode are universal. The result is also extended to numerical P systems with an upperthreshold, by proving the equivalence of the numerical P systems with lower- and upper-thresholds.

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