Affiliations: Key Laboratory of Image Processing and Intelligent Control, Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, Hubei, People's Republic of China. lqpan@mail.hust.edu.cn, junwangjf@gmail.com | Leiden Institute of Advanced Computer Science, Leiden University, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands. hoogeboom@liacs.nl
Note: [] also affiliated to LIACS, Leiden University
Note: [] Address for correspondence: Leiden Institute of Advanced Computer Science, Leiden University, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands
Abstract: In a biological system, if a long enough time interval is given, an enabled chemical reaction will finish its reaction in the given time interval. With this motivation, it is natural to impose a bound on the time interval when an enabled spiking rule in a spiking neural P system (SN P system, for short) remains unused. In this work, a new working mode of SN P systems is defined, which is called limited asynchronous mode. In an SN P system working in limited asynchronous mode, if a rule is enabled at some step, this rule is not obligatorily used. From this step on, if the unused rule may be used later, it should be used in the given time interval. If further spikes make the rule non-applicable, then the computation continues in the new circumstances. The computation result of a computation in an SN P system working in limited asynchronous mode is defined as the total number of spikes sent into the environment by the system. It is proved that limited asynchronous SN P systems with standard spiking rules are universal. If the number of spikes present in each neuron of a limited asynchronous SN P system with standard spiking rules is bounded during a computation, then the power of a limited asynchronous SN P system with standard spiking rules falls drastically, and we get a characterization of semilinear sets of numbers.
