On Distributed Solution to SAT by Membrane Computing


Tissue P systems with evolutional communication rules and cell division (TPec, for short) are a class of bio-inspired parallel computational models, which can solve NP-complete problems in a feasible time. In this work, a variant of TPec, called $k$-distributed tissue P systems with evolutional communication and cell division ($k\text{-}\Delta_{TP_{ec}}$, for short) is proposed. A uniform solution to the SAT problem by $k\text{-}\Delta_{TP_{ec}}$ under balanced fixed-partition is presented. The solution provides not only the precise satisfying truth assignments for all Boolean formulas, but also a precise amount of possible such satisfying truth assignments. It is shown that the communication resource for one-way and two-way uniform $k$-P protocols are increased with respect to $k$; while a single communication is shown to be possible for bi-directional uniform $k$-P protocols for any $k$. We further show that if the number of clauses is at least equal to the square of the number of variables of the given boolean formula, then $k\text{-}\Delta_{TP_{ec}}$ for solving the SAT problem are more efficient than TPec as show in \cite{bosheng2017}; if the number of clauses is equal to the number of variables, then $k\text{-}\Delta_{TP_{ec}}$ for solving the SAT problem work no much faster than TPec.


[1] Adorna, H., Paun, Gh. Pérez-Jiménez, M.J. (2010): On Communication Complexity in Evolution-Communication P Systems, Rom. J. Inf. Sci. Tech., 13(2), 113–130, 2010.

[2] Alhazov, A. (2004): On Determinism of Evolution-Communication P Systems, J. Univers. Comput. Sci. 10(5), 502–508, 2004.

[3] Bu-o, K., Adorna, H., Pan, L. Song, B.(2017): Communicaton Complexity of Distributed Tissue-Like P Systems for Solving SAT Problem, Proc. of the 18th International Conference on Membrane Computing, Bradford, UK, 373–383, 2017.

[4] Bu-o, K. Cabarle, F., Adorna, H., Calabia, M.(2018): Solving N-Queens Problem using dP Systems with Active Membranes, Theor. Comput. Sci., 2018.

[5] Cavaliere, M. (2003): Evolution-Communication P Systems, In: Paun, Gh. et al, (Eds.) LNCS, Springer, Heidelberg, 2597, 134–145, 2003.

[6] Csuhaj-Varjú, E., Margenstern, M., Vazil, G., Verlan, S. (2007): On Small Universal Antiport P System, Theor. Comput. Sci., 372(2-3), 152–164, 2007.

[7] Csuhaj-Varjú, E., Vaszil, G. (2012): Finite dP Automata Versus Multi-head Finite Automata. In: Gheorghe, M. et al. (Eds.): LNCS, Springer, Heidelberg, 7184, 120–138, 2012.

[8] Díaz-Pernil, D., Pe-a-Cantillana, F., Gutiérrez-Naranjo, M.A. (2013): A Parallel Algorithm for Skeletonizing Images by Using Spiking Neural P Systems, Neurocomputing, 115, 81–91, 2013.

[9] Dzitac, I. (2015): Impact of Membrane Computing and P Systems in ISI WoS. Celebrating the 65th Birthday of Gheorghe Paun, Int. J. Comput. Commun, 10(5), 617–626, 2015.

[10] Elias, S., Gokul, V, Krithivasan, K., Gheorghe, M., Zhang, G. (2012): A Variant of Distributed P Systems for Real Time Cross Layer Optimization, J. Univers. Comput. Sci., 18(13), 1760–1781, 2012.

[11] Frisco, P., Govan, G., Leporati, A. (2012): Asynchronous P Systems with Active Membranes, Theor. Comput. Sci., 429, 74–86, 2012.

[12] Gazdag, Z. (2014): Solving SAT by P Systems with Active Membranes in Linear Time in the Number of Variables. In: Alhazov, A. et al. (Eds.) LNCS, Springer, Heidelberg, 8340, 189–205, 2014.

[13] Gutiérrez-Naranjo, M.A., Martínez-del-Amor, M.A., Pérez-Jurtado, I., Pérez-Jiménez, M.J. (2009): Solving N-Queens Puzzle with P Systems. In: Proc. of the 7th Brainstorming Week on Membrane Computing, Sevilla, Spain, 199–210, 2009.

[14] Hernandez, N., Juayong, R., Adorna, H. (2014): On the Communication Complexity of Some Hard Problems in ECPe Systems. In: Alhazov, A. et al. (Eds.): LNCS, Springer, Heidelberg, 8340, 206–224, 2014.

[15] Macías-Ramos, L.F., Valencia-Cabrera, L., Song, B., Pan, L., Pérez-Jiménez, M.J. (2015): A P-Lingua Based Simulator for P Systems with Symport/Antiport Rules, Fund. Informa., 139(2), 211–277, 2015.

[16] Martínez-del-Amor, M.A., García-Quismondo, M., Macías-Ramos, L.F., Valencia-Cabrera, L., Riscos-Nú-ez, A., Pérez-Jiménez, M.J. (2015): Simulating P Systems on GPU Devices: A Survey, Fund. Informa., 136(3), 269–284, 2015.

[17] Pan, L., Paun, Gh. (2009): Spiking Neural P Systems with Anti-Spikes, Int. J. Comput. Commun., 4(3), 273–282, 2009.

[18] Pan, L., Pérez-Jiménez, M.J. (2010): Computational Complexity of Tissue-Like P Systems, J. Complexity, 26(3), 296–315, 2010.

[19] Paun, Gh. (2000): Computing with Membranes, J. Comput. Syst. Sci., 61(1), 108–143, 2000.

[20] Paun, Gh. (2016): Membrane Computing and Economics: A General View, Int. J. Comput. Commun., 11(1), 105–112, 2016.

[21] Paun, Gh., Pérez-Jiménez, M.J. (2010): Solving Problem in a DistributedWay in Membrane Computing: dP Sytems, Int. J. Comput. Commun., 5, 238–259, 2010.

[22] Paun, Gh., Pérez-Jiménez, M.J. (2012): An Infinite Hierarchy of Languages Defined by dP Systems, Theor. Comput. Sci., 431, 4–12, 2012.

[23] Paun, Gh. Rozenberg, G., Salomaa, A. (Eds.)(2010): The Oxford Handbook of Membrane Computing, Oxford University Press, New York, 2010.

[24] Peng, H., Wang, J., Pérez-Jiménez, M.J., Riscos-Nú-ez, A. (2015): An Unsupervised Learning Algorithm for Membrane Computing, Inf. Sci., 304, 80–91, 2015.

[25] Song, T., Pan, L. (2016): Spiking Neural P Systems with Request Rules, Neurocomputing, 193, 193–200, 2016.

[26] Song, T., Pan, L., Paun, Gh. (2013): Asynchronous Spiking Neural P Systems with Local Synchronization, Inf. Sci. 219, 197–207, 2013.

[27] Song, B., Pan, L. (2016): The Computational Power of Tissue-Like P Systems with Promoters, Theor. Comput. Sci., 641, 43–52, 2016.

[28] Song, B., Song, T., Pan, L. (2017): A Time-Free Uniform Solution to Subset Sum Problem by Tissue P Systems with Cell Division, Math. Struct. Comp. Sci., 27(1), 17–32, 2017.

[29] Song, B., Zhang, C., Pan, L. (2017): Tissue-Like P Systems with Evolutional Symport/Antiport Rules, Inf. Sci., 378, 177–193, 2017.

[30] Valencia-Cabrera, L., Orellana-Martín, D., Martínez-del-Amor, M.A., Riscos-Nú-ez, A., Pérez-Jiménez, M.J. (2017): Cooperation in Transport of Chemical Substances: A Complexity Approach within Membrane Computing, Fund. Informa., 154(1-4), 373–385, 2017.

[31] Valencia-Cabrera, L., Orellana-Martín, D., Martínez-del-Amor, M.A., Riscos-Nú-ez, A., Pérez-Jiménez, M.J. (2017): Reaching Efficiency through Collaboration in Membrane Systems: Dissolution, Polarization and Cooperation, Theor. Comput. Sci., 701, 226–234, 2017.

[32] Valencia-Cabrera, L., Wu, T., Zhang, Z.,Pan, L., Pérez-Jiménez, M.J. (2016): A Simulation Software Tool for Cell-Like Spiking Neural P Systems, Rom. J. Inf. Sci. Tech., 20(1), 71–84, 2016.

[33] Wu, T., Zhang, Z., Paun, Gh., Pan, L. (2016): Cell-Like Spiking Neural P Systems, Theor. Comput. Sci., 623, 180–189, 2016.

[34] Yao, A.C. (1979): Some Complexity Questions Related to Distributed Computing, In: Proceedings of the eleventh annual ACM symposium on Theory of computing, 209–213, 1979.

[35] Zandron, C., Leporati, A., Ferretti, C., Mauri, G., Pérez-Jiménez, M.J. (2008): On the Computational Efficiency of Polarizationless Recognizer P Systems with Strong Division and Dissolution, Fund. Informa., 87(1), 79–91, 2008.

[36] Zhang, G., Rong, H., Neri, F., Pérez-Jiménez, M.J. (2014): An Optimization Spiking Neural P System for Approximately Solving Combinatorial Optimization Problems, Int. J. Neural Syst., 24, 1–16, 2014.

[37] Zhang, X., Pan, L., Paun, A. (2015): On the Universality of Axon P Systems, IEEE T. Neur. Net. Lea., 26(11), 2816-2829, 2015.
How to Cite
ADORNA, Henry N.; PAN, Linqiang; SONG, Bosheng. On Distributed Solution to SAT by Membrane Computing. INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL, [S.l.], v. 13, n. 3, p. 303-320, may 2018. ISSN 1841-9844. Available at: <http://univagora.ro/jour/index.php/ijccc/article/view/3217>. Date accessed: 09 july 2020. doi: https://doi.org/10.15837/ijccc.2018.3.3217.