Time-Free Cell-Like P Systems with Multiple Promoters/Inhibitors

Abstract Cell-like P systems with promoters/inhibitors (PIC-P systems) are a class of distributed and parallel computing models inspired by the function of regulating biochemical reactions by enzymes in biological cells. In PIC-P systems, each evolution rule (rule for short) can be associated with one promoter/inhibitor which helps control the evolution process of objects. In this work, we propose a novel variant of PIC-P systems, called time-free cell-like P systems with multi-promoters/inhibitors (time-free MPIC-P systems for short). In such systems, each rule can be associated with multiple promoters/inhibitors, and the execution time of each rule is extended from one time unit to a random number of time units. These two characters make the time-free MPIC-P systems closer to biological cells. We also investigate the computational power of time-free MPIC-P systems. As results, it is achieved by simulating the matrix grammar that such systems can generate the set of lengths of recursively enumerable languages, that is, Turing universality can be achieved. This indicates that the time-free working mode will not reduce the computational power of PIC-P systems, by using multiple promoters/inhibitors.