The decision problems solved in polynomial time by P systems with elementary active membranes are known to include the class ^#. This consists of all the problems solved by polynomial-time deterministic Turing machines with polynomial-time counting oracles. In this paper we prove the reverse inclusion by simulating P systems with this kind of machines: this proves that the two complexity classes coincide, finally solving an open problem by Păun on the power of elementary division. The equivalence holds for both uniform and semi-uniform families of P systems, with or without membrane dissolution rules. Furthermore, the inclusion in ^# also holds for the P systems involved in the P conjecture (with elementary division and dissolution but no charges), which improves the previously known upper bound .

Simulating elementary active membranes with an application to the P conjecture

Manzoni Luca;
2014-01-01

Abstract

The decision problems solved in polynomial time by P systems with elementary active membranes are known to include the class ^#. This consists of all the problems solved by polynomial-time deterministic Turing machines with polynomial-time counting oracles. In this paper we prove the reverse inclusion by simulating P systems with this kind of machines: this proves that the two complexity classes coincide, finally solving an open problem by Păun on the power of elementary division. The equivalence holds for both uniform and semi-uniform families of P systems, with or without membrane dissolution rules. Furthermore, the inclusion in ^# also holds for the P systems involved in the P conjecture (with elementary division and dissolution but no charges), which improves the previously known upper bound .
2014
978-3-319-14369-9
978-3-319-14370-5
http://springerlink.com/content/0302-9743/copyright/2005/
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/2947964
 Avviso

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 26
  • ???jsp.display-item.citation.isi??? 22
social impact