Abstract
The decision problems solved in polynomial time by P systems with elementary active membranes are known to include the class \(\mathbf{P}^{\# \mathbf{P}}\). 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 \(\mathbf{P}^{\# \mathbf{P}}\) 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 \(\mathbf{PSPACE}\).
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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Leporati, A., Manzoni, L., Mauri, G., Porreca, A.E., Zandron, C. (2014). Simulating Elementary Active Membranes. In: Gheorghe, M., Rozenberg, G., Salomaa, A., Sosík, P., Zandron, C. (eds) Membrane Computing. CMC 2014. Lecture Notes in Computer Science(), vol 8961. Springer, Cham. https://doi.org/10.1007/978-3-319-14370-5_18
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DOI: https://doi.org/10.1007/978-3-319-14370-5_18
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