Abstract
In this paper we present a method for solving the NP-complete SAT problem using the type of P systems that is defined in [9]. The SAT problem is solved in O(nm) time, where n is the number of boolean variables and m is the number of clauses for a instance written in conjunctive normal form. Thus we can say that the solution for each given instance is obtained in linear time. We succeeded in solving SAT by a uniform construction of a deterministic P system which uses rules involving objects in regions, proteins on membranes, and membrane division. We also investigate the computational power of the systems with proteins on membranes and show that the universality can be reached even in the case of systems that do not even use the membrane division and have only one membrane.
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References
Alhazov, A.: Solving SAT by symport/antiport P systems with memebrane division. In: Gutierrez-Naranjo, M.A., Păun, G., Perez-Jimenez, M.J. (eds.) Cellular Computing. Complexity Aspects, pp. 1–6. Fenix Editora, Sevilla (2005)
Alhazov, A., Margenstern, M., Rogozhin, V., Rogozhin, Y., Verlan, S.: Communicative P systems with minimal cooperation. In: Mauri, G., Păun, G., Jesús Pérez-Jímenez, M., Rozenberg, G., Salomaa, A. (eds.) WMC 2004. LNCS, vol. 3365, pp. 161–177. Springer, Heidelberg (2005)
Busi, N.: On the computational power of the mate/bud/drip brane calculus: interleaving vs, maximal parallelism. In: Freund, R., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2005. LNCS, vol. 3850, pp. 144–158. Springer, Heidelberg (2006)
Cardelli, L.: Brane calculi – interactions of biological membranes. In: Danos, V., Schachter, V. (eds.) CMSB 2004. LNCS (LNBI), vol. 3082, pp. 257–278. Springer, Heidelberg (2005)
Ibarra, O.H., Păun, A.: Counting time in computing with cells. In: Carbone, A., Pierce, N.A. (eds.) DNA 2005. LNCS, vol. 3892, pp. 112–128. Springer, Heidelberg (2006)
Leporati, A., Zandron, C.: A family of P systems which solve 3-SAT. In: Gutierrez-Naranjo, M.A., Păun, G., Perez-Jimenez, M.J. (eds.) Cellular Computing. Complexity Aspects, pp. 247–256. Fenix Editora, Sevilla (2005)
Minsky, M.L.: Computation: Finite and Infinite Machines. Prentice Hall, Englewood Cliffs (1967)
Păun, A., Păun, G.: The power of communication: P systems with symport/antiport. New Generation Computing 20, 3, 295–306 (2002)
Păun, A., Popa, B.: P systems with proteins on membranes. Fundamenta Informaticae (accepted, 2006)
Păun, G.: Membrane Computing – An Introduction. Springer, Berlin (2002)
Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages. Springer, Berlin (1987)
The P Systems Website: http://psystems.disco.unimib.it
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Păun, A., Popa, B. (2006). P Systems with Proteins on Membranes and Membrane Division. In: Ibarra, O.H., Dang, Z. (eds) Developments in Language Theory. DLT 2006. Lecture Notes in Computer Science, vol 4036. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11779148_27
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DOI: https://doi.org/10.1007/11779148_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-35428-4
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