Cell-like recognizing membrane systems are computational devices in the framework of membrane computing inspired from the structure of living cells, where biological membranes are arranged hierarchically. In this paper tissue-like recognizing membrane systems are presented. The idea is to consider that membranes are placed in the nodes of a graph, mimicking the cell intercommunication in tissues. In this context, polynomial complexity classes associated with recognizing membrane systems can be defined. We recall the definition for cell-like systems, and we introduce the corresponding complexity classes for the tissue-like case. Moreover, in this paper two efficient solutions to the satisfiability problem are analyzed and compared from a complexity point of view. © 2009 Wiley Periodicals, Inc.