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 [Formula presented], where [Formula presented] 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 [Formula presented]. Such results are typically proved by showing how elements of a family [Formula presented] of P systems can be embedded into P systems simulating Turing machines, which exploit the elements of [Formula presented] as subroutines. Here we focus on the latter construction, providing a description that, by abstracting from the technical details which depend on the specific variant of P system, describes a general strategy for proving closure under exponentiation. We also provide an example implementation using polarizationless P systems with active membranes and minimal cooperation.
Leporati, A., Manzoni, L., Mauri, G., Porreca, A., Zandron, C. (2020). Subroutines in P systems and closure properties of their complexity classes. THEORETICAL COMPUTER SCIENCE, 805, 193-205 [10.1016/j.tcs.2018.06.012].
Subroutines in P systems and closure properties of their complexity classes
Leporati, A
;Manzoni, L
;Mauri, G
;Zandron, C
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 [Formula presented], where [Formula presented] 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 [Formula presented]. Such results are typically proved by showing how elements of a family [Formula presented] of P systems can be embedded into P systems simulating Turing machines, which exploit the elements of [Formula presented] as subroutines. Here we focus on the latter construction, providing a description that, by abstracting from the technical details which depend on the specific variant of P system, describes a general strategy for proving closure under exponentiation. We also provide an example implementation using polarizationless P systems with active membranes and minimal cooperation.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.