2020 **Abstract:** The literature on membrane computing describes several variants of P systems whose complexity classes C are "closed under exponentiation", that is, they satisfy the inclusion P C ⊆ C, where P C is the class of problems solved by polynomial-time Turing machines with oracles for problems in C. This closure automatically implies closure under many other operations, such as regular operations (union, concatenation, Kleene star), intersection, complement, and polynomial-time mappings, which are inherited from P. Su…

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“…It is quite easy to simulate efficiently (actually, in linear time) a deterministic Turing machine working in polynomial time by means of a uniform family of P systems [8].…”

confidence: 99%

“…It is quite easy to simulate efficiently (actually, in linear time) a deterministic Turing machine working in polynomial time by means of a uniform family of P systems [8].…”

confidence: 99%

“…Thus, a single membrane (or a number of membranes obtained by division of a single initial one, in the case of nondeterminism) can efficiently simulate a polynomial-size tape Turing machine and, in particular, a Turing machine working in polynomial time. On the other hand, using several nested membranes it is possible to efficiently simulate oracle queries [8]. With bidirectional P systems (i.e., standard P systems using both send-in and send-out rules) the simulation of the Turing machine is paused, then one usually sends the query string into a child membrane, where another Turing machine for the oracle language is simulated, possibly using membrane division; the answer is then sent out and the simulation of the original Turing machine is resumed.…”

confidence: 99%

“…The computational complexity of (tissue) P systems with membrane division or membrane separation has also been investigated. In [58], it was proved that P systems with active membranes characterize PSPACE, that is, the class of problems solvable by P systems with active membranes is equal to PSPACE (further studied in [16][17][18][19]57]). In [55,56], an upper bound of the computational power of tissue P systems with cell separation or cell division is provided, respectively; it was thus shown that the class of problems that are solved in polynomial time by tissue P systems with cell separation or cell division is contained in the class PSPACE.…”

confidence: 99%

“…Note the use of oracles and complexity classes of the form , containing languages recognizable by polynomial-time Turing machines with oracles for languages in . Such classes allow for a general way of proving their closure under several operations (union, concatenation, Kleene star, intersection, complement...) implied by their closure under the so-called exponentiation, i.e., ⊆ [27]. The complexity class PSPACE plays an important role in the theory of parallel computing.…”

confidence: 99%