Looking for small universal computing devices is a natural and well investigated topic in computer science. Recently, this topic started to be considered also in the framework of (synchronized) spiking neural P systems. In this work, it is focused on small universal spiking neural P systems working in a non-synchronized manner. Specifically, it is proved that there is an asynchronous spiking neural P system with 76 neurons that is equivalent to a universal register machine for computing functions. As generator of sets of numbers, a universal asynchronous spiking neural P system with 75 neurons is constructed.
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