Abstract
In this paper we introduce a membrane system (named λP systems) in which the computation is performed through certain operations on the tree structure of the membranes. The objects within the membranes play the role of catalysts for the operations. The result of the computation is the final configuration of the system. We show that λP systems can simulate pure λ-calculus and so they have universal computational power. We also show that NP-complete problems can be solved in polynomial time in this way by showing that 3SAT is solvable in linear time with linear input.