Abstract
We prove that a uniform family of P systems with active membranes, where division rules only operate on elementary membranes and dissolution rules are avoided, can be used to solve the following PP-complete decision problem in polynomial time: given a Boolean formula of m variables in 3CNF, do at least \(\sqrt{2^m}\) among the 2m possible truth assignments satisfy it? As a consequence, the inclusion \(\mathbf{PP} \subseteq \mathbf{PMC}_{\mathcal{AM}(\mathrm{-d,-n})}\) holds: this provides an improved lower bound on the class of languages decidable by this kind of P systems.
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Porreca, A.E., Leporati, A., Mauri, G., Zandron, C. (2010). P Systems with Elementary Active Membranes: Beyond NP and coNP. In: Gheorghe, M., Hinze, T., Păun, G., Rozenberg, G., Salomaa, A. (eds) Membrane Computing. CMC 2010. Lecture Notes in Computer Science, vol 6501. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18123-8_26
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DOI: https://doi.org/10.1007/978-3-642-18123-8_26
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