April 13, 2012 11:57 WSPC/INSTRUCTION FILE paper International Journal of Foundations of Computer Science c  World Scientific Publishing Company P SYSTEMS WITH ACTIVE MEMBRANES WORKING IN POLYNOMIAL SPACE ANTONIO E. PORRECA, ALBERTO LEPORATI, GIANCARLO MAURI, CLAUDIO ZANDRON Dipartimento di Informatica, Sistemistica e Comunicazione Universit` a degli Studi di Milano-Bicocca Viale Sarca 336/14, 20126 Milano, Italy {porreca,leporati,mauri,zandron}@disco.unimib.it Received (Day Month Year) Accepted (Day Month Year) Communicated by (xxxxxxxxxx) We prove that recognizer P systems with active membranes using polynomial space characterize the complexity class PSPACE. This result holds for both confluent and nonconfluent systems, and independently of the use of membrane division rules. Keywords : Membrane computing; complexity theory; space complexity. 1991 Mathematics Subject Classification: 68Q10, 68Q15 1. Introduction P systems with active membranes [2] are a variant of P systems where the mem- branes affect the applicability of rules during the computation. Furthermore, the membranes can also grow exponentially in number, via division rules, allowing us to solve computationally hard problems in polynomial time. In this paper we prove that P systems with active membranes working in poly- nomial space solve exactly the problems in PSPACE, even when strong features such as division rules and nonconfluence are used. The proof technique is based on a variant of two previously published simulation algorithms [8, 9]. 2. Preliminaries We assume that the reader is familiar with basic terminology and results concerning P systems with active membranes (see [3], chapters 11–12 for a survey). Definition 1. A P system with active membranes of the initial degree d ≥ 1 is a tuple Π = (Γ, Λ, µ, w 1 ,...,w d ,R), where: • Γ is a finite alphabet of symbols, also called objects; • Λ is a finite set of labels for the membranes; 1