Abstract
We consider the possibility of using spiking neural P systems for solving computationally hard problems, under the assumption that some (possibly exponentially large) pre-computed resources are given in advance. In particular, we propose two uniform families of spiking neural P systems which can be used to address the NP-complete problems sat and 3-sat, respectively. Each system in the first family is able to solve all the instances of sat which can be built using n Boolean variables and m clauses, in a time which is quadratic in n and linear in m. Similarly, each system of the second family is able to solve all the instances of 3-sat that contain n Boolean variables, in a time which is cubic in n. All the systems here considered are deterministic.
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Acknowledgments
The authors would like to thank the anonymous referees, whose suggestions have allowed us to improve a previous version of this paper. The work of Tseren-Onolt Ishdorj was supported by Academy of Finland, project 122426. Alberto Leporati was partially supported by the project “Azioni Integrate Italia-Spagna - Theory and Practice of Membrane Computing” (Acción Integrada Hispano–Italiana HI 2005-0194).
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Ishdorj, TO., Leporati, A. Uniform solutions to SAT and 3-SAT by spiking neural P systems with pre-computed resources. Nat Comput 7, 519–534 (2008). https://doi.org/10.1007/s11047-008-9081-0
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DOI: https://doi.org/10.1007/s11047-008-9081-0