P Systems with Symport/Antiport and Time Hitesh Nagda 1 , Andrei P˘ aun 1,2 , and Alfonso Rodr´ ıguez-Pat´on 2 1 Department of Computer Science/IfM, Louisiana Tech University P.O. Box 10348, Ruston, LA 71272, USA {hhn002, apaun}@latech.edu 2 Universidad Polit´ ecnica de Madrid - UPM, Facultad de Inform´atica Campus de Montegancedo S/N, Boadilla del Monte, 28660 Madrid, Spain arpaton@fi.upm.es Abstract. We consider symport/antiport P systems using the time as the support for the output of a computation. We describe and study the properties of “timed symport/antiport systems”, showing that this new model of membrane systems based on time has more power/flexibility, and thus allows us to improve previous universality results. We were able to improve or match the best results concerning the symport/antiport systems which consider the output as originally defined as the number of molecules found in a pre-defined elementary membrane in the halting configuration of the system. 1 Introduction We continue the work on symport/antiport P systems which were considered in a series of recent papers. We refer the interested reader to [1], [2], [5], [6], [11], for basic definitions and results in this area. Briefly, the systems that we consider in this paper extend the original definition by using the paradigm of time as the output of a computation as previously introduced in [4] and [8]. The idea originates in [12] as Problem W; the novelty is that instead of the “standard” way to output, like the multiplicities of objects found at the end at the computation in a distinguished membrane as it was defined in the model from [11], it seems more “natural” to consider certain events (i.e., configurations) that may occur during a computation and to relate the output of such a computation with the time interval between such distinguished configurations. Our system will compute a set of numbers similarly with the case of “normal” symport/antiport systems as defined in [11], but the benefit of the current setting is that the computation and the observance of the output are now close to the biology and to the tools used for cell biology (fluorescence microscopy, FACS). The model of the “timed” P system that we investigate here is the symport/antiport P system. We note that such a “timed” approach could be applied also to other types of P systems. Actually the spiking neural P systems ([9], [14]) use a similar idea: the output of such a system is the time elapsed between two spikes of a pre-defined “output” neuron. Going back to the symport/antiport model, we are studying another way of viewing the output of such a system; the motivation comes from the fact H.J. Hoogeboom et al. (Eds.): WMC 7, LNCS 4361, pp. 463–476, 2006. c  Springer-Verlag Berlin Heidelberg 2006