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.
Articolo in rivista - Articolo scientifico
Scientifica
Closure under exponentiation; Membrane computing; Oracle machines;
Membrane computing; Oracle machines; Theoretical Computer Science; complexity classes
English
Anno_pub:2020-
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].
Leporati, A; Manzoni, L; Mauri, G; Porreca, A; Zandron, C
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/211922
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