A Semantic Investigation of Spiking Neural P Systems

  • Gabriel Ciobanu
  • Eneia Nicolae TodoranEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11399)


We present a metric denotational semantics for an experimental concurrent language inspired by the spiking neural P systems. At syntactic level, the language provides constructions for specifying the neurons, synapses and rules with time delays defining a spiking neural P system. The denotational semantics presented in this paper is designed by using continuations. We employ metric spaces, including a metric powerdomain to describe the nondeterministic behaviour. Our denotational semantics describes accurately the time delays between firings and spikings, the nondeterministic behaviour and the synchronized functioning that are specific of a spiking neural P system. An implementation in the functional language Haskell is also provided; it can be tested and evaluated, being available for software experiments.


  1. 1.
    Alexandru, A., Ciobanu, G.: Mathematics of multisets in the Fraenkel-Mostowski framework. Bull. Math. Soc. Sci. Math. Roumanie 58(106), 3–18 (2015)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Alhazov, A., Freund, R., Oswald, M., Slavkovik, M.: Extended spiking neural P systems. In: Hoogeboom, H.J., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2006. LNCS, vol. 4361, pp. 123–134. Springer, Heidelberg (2006). Scholar
  3. 3.
    Aman, B., Ciobanu, G.: Automated verification of stochastic spiking neural P systems. In: Rozenberg, G., Salomaa, A., Sempere, J.M., Zandron, C. (eds.) CMC 2015. LNCS, vol. 9504, pp. 77–91. Springer, Cham (2015). Scholar
  4. 4.
    America, P., Rutten, J.J.M.M.: Solving reflexive domain equations in a category of complete metric spaces. J. Comput. Syst. Sci. 39, 343–375 (1989)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Appel, A.W.: Compiling with Continuations. Cambridge University Press, Cambridge (2007)Google Scholar
  6. 6.
    de Bakker, J.W., de Vink, E.P.: Control Flow Semantics. MIT Press, Cambridge (1996)zbMATHGoogle Scholar
  7. 7.
    Barendregt, H.P.: The Lambda Calculus, Its Syntax and Semantics. Elsevier, Amsterdam (1984)zbMATHGoogle Scholar
  8. 8.
    Cavaliere, M., Mura, I.: Experiments on the reliability of stochastic spiking neural P systems. Nat. Comput. 7, 453–470 (2008)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Chen, H., Ionescu, M., Isidorj, T.O., Păun, A., Păun, Gh., Pérez-Jiménez, M.J.: Spiking neural P systems with extended rules: universality and languages. Nat. Comput. 7, 147–166 (2008)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Ciobanu, G.: Semantics of the P systems. In: Handbook of Membrane Computing, pp. 413–436. Oxford University Press (2010)Google Scholar
  11. 11.
    Ciobanu, G., Todoran, E.N.: Continuation semantics for asynchronous concurrency. Fundam. Inform. 131(3–4), 373–388 (2014)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Ciobanu, G., Todoran, E.N.: Continuation passing semantics for membrane systems. In: Leporati, A., Rozenberg, G., Salomaa, A., Zandron, C. (eds.) CMC 2016. LNCS, vol. 10105, pp. 165–176. Springer, Cham (2017). Scholar
  13. 13.
    Ciobanu, G., Todoran, E.N.: Denotational semantics of membrane systems by using complete metric spaces. Theor. Comput. Sci. 701, 85–108 (2017)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Ionescu, M., Păun, Gh., Yokomori, T.: Spiking neural P systems. Fundam. Inform. 71, 279–308 (2006)Google Scholar
  15. 15.
    Ionescu, M., Păun, Gh., Pérez-Jiménez, M.J., Rodriguez-Patón, A.: Spiking neural P systems with several types of spikes. Int. J. Comput. Commun. Control 6, 647–655 (2011)CrossRefGoogle Scholar
  16. 16.
    Ishdorj, T.O., Leporati, A.: Uniform solutions to SAT and 3-SAT by spiking neural P systems with pre-computed resources. Nat. Comput. 7, 519–534 (2008)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Jech, T.: Set Theory. Springer, Heidelberg (2002)zbMATHGoogle Scholar
  18. 18.
    Leporati, A., Zandron, C., Ferretti, C., Mauri, G.: On the computational power of spiking neural P systems. Int. J. Unconv. Comput. 5, 459–473 (2009)Google Scholar
  19. 19.
    Păun, Gh.: Membrane Computing: An Introduction. Springer, Heidelberg (2002).
  20. 20.
    Jones, S.P., Hughes, J. (eds.): Report on the Programming Language Haskell 98: A Non-Strict Purely Functional Language (1999).
  21. 21.
    Pierce, B.: Types and Programming Languages. MIT Press, Cambridge (2002)zbMATHGoogle Scholar
  22. 22.
    Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages, vol. 3. Springer, Heidelberg (1998)Google Scholar
  23. 23.
    Todoran, E.N.: Metric semantics for synchronous and asynchronous communication: a continuation-based approach. Electron. Notes Theor. Comput. Sci. 28, 101–127 (2000)CrossRefGoogle Scholar
  24. 24.
    WWW: Haskell implementation of the denotational semantics presented in this paper (2018).

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Romanian Academy, Institute of Computer ScienceIaşiRomania
  2. 2.A.I. Cuza University of IaşiIaşiRomania
  3. 3.Technical University, Department of Computer ScienceCluj-NapocaRomania

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