Abstract
We prove that polynomial-time tissue P systems with cell division or cell separation can be simulated efficiently by Turing machines with oracles for counting problems. This shows that the corresponding complexity classes are included in \(\mathbf{P }^{\varvec{\#}\mathbf{P }}\), thus improving, under standard complexity theory assumptions, the previously known upper bound \(\mathbf{PSPACE }\).
This work was partially supported by Università degli Studi di Milano-Bicocca, FA 2013: “Complessità computazionale in modelli di calcolo bioispirati: Sistemi a membrane e sistemi di reazioni”.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Since communication rules are applied in a maximally parallel way, this restriction avoids the situation where infinitely many objects from the environment simultaneously enter a cell.
- 2.
This can be performed in polynomial time even if m is exponential, as it suffices to guess \(\varTheta (\log m)\) nondeterministic bits.
References
Alhazov, A., Martín-Vide, C., Pan, L.: Solving a PSPACE-complete problem by recognizing P systems with restricted active membranes. Fundamenta Informaticae 58(2), 67–77 (2003)
Leporati, A., Manzoni, L., Mauri, G., Porreca, A.E., Zandron, C.: Membrane division, oracles, and the counting hierarchy. Fundamenta Informaticae 138(1–2), 97–111 (2015)
Leporati, A., Manzoni, L., Mauri, G., Porreca, A.E., Zandron, C.: Simulating elementary active membranes with an application to the P conjecture. In: Gheorghe, M., Rozenberg, G., Salomaa, A., Sosík, P., Zandron, C. (eds.) CMC 2014. LNCS, vol. 8961, pp. 284–299. Springer, Heidelberg (2014)
Martín-Vide, C., Paun, G., Pazos, J., Rodríguez-Patón, A.: Tissue P systems. Theoret. Comput. Sci. 296(2), 295–326 (2003)
Murphy, N., Woods, D.: The computational power of membrane systems under tight uniformity conditions. Nat. Comput. 10(1), 613–632 (2011)
Pan, L., Pérez-Jiménez, M.J.: Computational complexity of tissue-like P systems. J. Complex. 26(3), 296–315 (2010)
Papadimitriou, C.H.: Computational Complexity. Addison-Wesley, Reading, Massachussets (1993)
Pérez-Jiménez, M.J.: The P versus NP problem from the membrane computing view. Eur. Rev. 22(01), 18–33 (2014)
Paun, G., Pérez-Jiménez, M.J., Riscos Núñez, A.: Tissue P systems with cell division. Int. J. Comput. Commun. Control 3(3), 295–303 (2008)
Sosík, P., Cienciala, L.: Computational power of cell separation in tissue P systems. Inf. Sci. 279, 805–815 (2014)
Sosík, P., Cienciala, L.: A limitation of cell division in tissue P systems by PSPACE. J. Comput. Syst. Sci. 81(2), 473–484 (2015)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Leporati, A., Manzoni, L., Mauri, G., Porreca, A.E., Zandron, C. (2015). Tissue P Systems Can be Simulated Efficiently with Counting Oracles. In: Rozenberg, G., Salomaa, A., Sempere, J., Zandron, C. (eds) Membrane Computing. CMC 2015. Lecture Notes in Computer Science(), vol 9504. Springer, Cham. https://doi.org/10.1007/978-3-319-28475-0_17
Download citation
DOI: https://doi.org/10.1007/978-3-319-28475-0_17
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-28474-3
Online ISBN: 978-3-319-28475-0
eBook Packages: Computer ScienceComputer Science (R0)