Skin Output in P Systems with Minimal Symport/Antiport and Two Membranes Artiom Alhazov 1,2 and Yurii Rogozhin 1,3 1 Institute of Mathematics and Computer Science Academy of Sciences of Moldova Str. Academiei 5, Chi¸ sin˘au, MD-2028 Moldova {artiom,rogozhin}@math.md 2 ˚ Abo Akademi University Department of Information Technologies Turku Center for Computer Science, FIN-20520 Turku, Finland aalhazov@abo.fi 3 Rovira i Virgili University, Research Group on Mathematical Linguistics, Pl. Imperial T`arraco 1, 43005 Tarragona, Spain Abstract. It is known that symport/antiport P systems with two mem- branes and minimal cooperation can generate any recursively enumerable sets of natural numbers using exactly one superfluous object in the out- put membrane, where the output membrane is an elementary membrane. In this paper we consider symport/antiport P systems where the output membrane is the skin membrane. In this case we prove an unexpected characterization: symport/antiport P systems (and purely symport P systems) with two membranes and minimal cooperation generate exactly the recursively enumerable sets of natural numbers. 1 Introduction P systems with symport/antiport rules, i.e., P systems with pure communica- tion rules assigned to membranes, first were introduced in [24]; symport rules move objects across a membrane together in one direction, whereas antiport rules move objects across a membrane in opposite directions. These operations are very powerful, i.e., P systems with symport/antiport rules have universal computational power with only one membrane, e.g., see [12], [15], [13]. A comprehensive overview of the most important results obtained in the area of P systems and tissue P systems with symport/antiport rules, with respect to the development of computational completeness results improving descriptional complexity parameters as the number of membranes and cells, the size of the rules, and the number of objects can be found in [1]. For instance, in [3] one obtains the exact characterization of NRE for sym- port/antiport P systems with three membranes and minimal cooperation and for corresponding purely symport P systems. In [5] one shows that if some P system with two membranes and with min- imal cooperation, i.e., a P system with symport/antiport rules of size one or a G. Eleftherakis et al. (Eds.): WMC8 2007, LNCS 4860, pp. 97–112, 2007. c  Springer-Verlag Berlin Heidelberg 2007