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

  • Authors:

  • Tseren-Onolt Ishdorj;Alberto Leporati

  • Affiliations:

  • Computational Biomodelling Laboratory, Department of Information Technologies, Åbo Akademi University, Turku, Finland 20520;Dipartimento di Informatica, Sistemistica e Comunicazione, Università degli Studi di Milano --- Bicocca, Milano, Italy 20126

  • Venue:
  • Natural Computing: an international journal
  • Year:
  • 2008

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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.