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

  • Authors:

  • Alberto Leporati;Giancarlo Mauri;Claudio Zandron;Gheorghe Păun;Mario J. Pérez-Jiménez

  • Affiliations:

  • Dipartimento di Informatica, Sistemistica e Comunicazione, Università degli Studi di Milano --- Bicocca, Milano, Italy 20126;Dipartimento di Informatica, Sistemistica e Comunicazione, Università degli Studi di Milano --- Bicocca, Milano, Italy 20126;Dipartimento di Informatica, Sistemistica e Comunicazione, Università degli Studi di Milano --- Bicocca, Milano, Italy 20126;Institute of Mathematics of the Romanian Academy, Bucharest, Romania 014700 and Research Group on Natural Computing, Department of Computer Science and Artificial Intelligence, University of Sevil ...;Research Group on Natural Computing, Department of Computer Science and Artificial Intelligence, University of Sevilla, Sevilla, Spain 41012

  • Venue:
  • Natural Computing: an international journal
  • Year:
  • 2009

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Abstract

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.