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”.
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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.
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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
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