Deadlock decidability in partial parallel P systems

In parallel rewriting P systems, the notion of deadlock is used to describe situations where evolution rules with different target indications are simultaneously applied on a common string. In this paper we claim that the generative power of partial parallel P systems (PPP, in short) with deadlock is equivalent to matrix grammars without appearance checking, and we prove that it is decidable whether or not a PPP will ever reach a deadlock configuration