Computing with membranes: P systems with worm-objects

We consider a combination of P systems with objects described by symbols with P systems with objects described by strings. Namely, we work with multisets of strings and consider as the result of a computation the number of strings in a given output membrane. The strings (also called worms) are processed by replication, splitting, mutation, and recombination; no priority among rules and no other ingredient is used. In these circumstances, it is proved that: (1) P systems of this type can generate all recursively enumerable sets of numbers; and moreover, (2) the Hamiltonian Path Problem in a directed graph can be solved in quadratic time, while the SAT problem can be solved in linear time. The interest of the latter result comes from the fact that it is the first time that a polynomial solution to an NP-complete problem has been obtained in the P system framework without making use of the (non-realistic) operation of membrane division.