Natural Computing

, 8:681 | Cite as

Uniform solutions to SAT and Subset Sum by spiking neural P systems

  • Alberto Leporati
  • Giancarlo Mauri
  • Claudio Zandron
  • Gheorghe PăunEmail author
  • Mario J. Pérez-Jiménez


We continue the investigations concerning the possibility of using spiking neural P systems as a framework for solving computationally hard problems, addressing two problems which were already recently considered in this respect: \({\tt Subset}\,{\tt Sum}\) and \({\tt SAT}.\) For both of them we provide uniform constructions of standard spiking neural P systems (i.e., not using extended rules or parallel use of rules) which solve these problems in a constant number of steps, working in a non-deterministic way. This improves known results of this type where the construction was non-uniform, and/or was using various ingredients added to the initial definition of spiking neural P systems (the SN P systems as defined initially are called here “standard”). However, in the \({\tt Subset}\,{\tt Sum}\) case, a price to pay for this improvement is that the solution is obtained either in a time which depends on the value of the numbers involved in the problem, or by using a system whose size depends on the same values, or again by using complicated regular expressions. A uniform solution to 3-\({\tt SAT}\) is also provided, that works in constant time.


Membrane computing Spiking neural P system SAT problem Subset sum problem Complexity 



The first three authors were partially supported by the project “Azioni Integrate Italia-Spagna—Theory and Practice of Membrane Computing” (Acción Integrada Hispano-Italiana HI 2005-0194). The work of the last two authors was supported by the project TIN 2006-13425 from the Ministerio de Educación y Ciencia of Spain, co-financed by FEDER funds, the Excellence project TIC-581 from the Junta de Andalucí a, and the Acción Integrada Hispano-Italiana HI 2005-0194. Gh. Păun was also partially supported by project BioMAT 2-CEx06-11-97/19.09.06.


  1. Chen H, Ionescu M, Ishdorj T-O (2006a) On the efficiency of spiking neural P systems. In: Proceedings of 8th international conference on electronics, information, and communication, Ulanbator, Mongolia, pp 49–52Google Scholar
  2. Chen H, Ishdorj T-O, Păun Gh, Pérez-Jiménez MJ (2006b) Spiking neural P systems with extended rules. In: Gutiérrez-Naranjo MA et al (eds) Proceedings of fourth brainstorming week on membrane computing, vol I. Fenix Editora, Sevilla, pp 241–265Google Scholar
  3. Garey MR, Johnson DS (1979) Computers and intractability. A guide to the theory on NP–Completeness. W.H. Freeman and Company, CA, USAGoogle Scholar
  4. Ibarra OH, Păun A, Păun Gh, Rodríguez-Patón A, Sosik P, Woodworth S (2007) Normal forms for spiking neural P systems. Theor Comput Sci 372(2–3):196–217zbMATHCrossRefGoogle Scholar
  5. Ionescu M, Păun Gh, Yokomori T (2006) Spiking neural P systems. Fundam Inform 71(2–3):279–308zbMATHGoogle Scholar
  6. Ionescu M, Păun Gh, Yokomori T (2007) Spiking neural P systems with an exhaustive use of rules. Int J Unconvent Comput 3(2):135–154Google Scholar
  7. Leporati A, Zandron C, Ferretti C, Mauri G (2007a) Solving numerical NP-complete problems with spiking neural P systems, In: Eleftherakis G, Kefalas P, Păun Gh, Rozenberg G, Salomaa A (eds) Membrane computing, International Workshop, WMC8, Thessaloniki, Greece, Selected and Invited Papers, LNCS 4860, Springer-Verlag, Berlin, pp 336–352Google Scholar
  8. Leporati A, Zandron C, Ferretti C, Mauri G (2007b) On the computational power of spiking neural P systems. Int J Unconvent Comput, in pressGoogle Scholar
  9. Păun Gh (2002) Membrane computing—an introduction. Springer, BerlinzbMATHGoogle Scholar
  10. Păun A, Păun Gh (2007) Small universal spiking neural P systems. BioSystems 90(1):48–60CrossRefGoogle Scholar
  11. Păun Gh, Pérez-Jiménez MJ, Rozenberg G (2002) Spike trains in spiking neural P systems. Int J Found Comp Sci 17(4):975–1002CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • Alberto Leporati
    • 1
  • Giancarlo Mauri
    • 1
  • Claudio Zandron
    • 1
  • Gheorghe Păun
    • 2
    • 3
    Email author
  • Mario J. Pérez-Jiménez
    • 3
  1. 1.Dipartimento di Informatica, Sistemistica e ComunicazioneUniversità degli Studi di Milano – BicoccaMilanoItaly
  2. 2.Institute of Mathematics of the Romanian AcademyBucharestRomania
  3. 3.Research Group on Natural Computing, Department of Computer Science and Artificial IntelligenceUniversity of SevillaSevillaSpain

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