Applied Mathematics & Information Sciences

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In membrane computing, spiking neural P systems (shortly called SN P systems) are a group of neural-like computing models inspired from the way spiking neurons communication in form of spikes. In previous works, SN P systems working in a nondeterministic manner have been used to solve numerical NP-complete problems, such as SAT, vertex cover, in feasible time. In these works, the application of any rule should complete in exactly one time unit, and the precise execution time of rules plays a crucial role on solving the problems in polynomial (or even in linear) time. However, the restriction does not coincide with the biological fact, since in biological systems, bio-chemical reactions may cost different execution time due to the external uncontrollable conditions. In this paper, we consider timed and time-free SN P systems, where the precise execution time of the rules is removed. To investigate the computational efficiency of time-free SN P systems, we solve Subset Sum problem by a family of uniform time-free SN P systems.

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