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Neural Computation

May 2011, Vol. 23, No. 5, Pages 1320-1342
(doi: 10.1162/NECO_a_00115)
© 2011 Massachusetts Institute of Technology
Time-Free Spiking Neural P Systems
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Different biological processes take different times to be completed, which can also be influenced by many environmental factors. In this work, a realistic definition of nonsynchronized spiking neural P systems (SN P systems, for short) is considered: during the work of an SN P system, the execution times of spiking rules cannot be known exactly (i.e., they are arbitrary). In order to establish robust systems against the environmental factors, a special class of SN P systems, called time-free SN P systems, is introduced, which always produce the same computation result independent of the execution times of the rules. The universality of time-free SN P systems is investigated. It is proved that these P systems with extended rules (several spikes can be produced by a rule) are equivalent to register machines. However, if the number of spikes present in the system is bounded, then the power of time-free SN P systems falls, and in this case, a characterization of semilinear sets of natural numbers is obtained.