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Uniform solutions to SAT and 3-SAT by spiking neural P systems with pre-computed resources

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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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Authors and Affiliations

  1. Computational Biomodelling Laboratory, Department of Information Technologies, Åbo Akademi University, Turku, 20520, Finland

    Tseren-Onolt Ishdorj

  2. Dipartimento di Informatica, Sistemistica e Comunicazione, Università degli Studi di Milano – Bicocca, Viale Sarca 336, 20126, Milano, Italy

    Alberto Leporati

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  1. Tseren-Onolt Ishdorj
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  2. Alberto Leporati
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Correspondence to Tseren-Onolt Ishdorj.

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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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