Asynchronous spiking neural P systems with local synchronization of rules

Asynchronous spiking neural P (AsynSN P) systems are a class of distributed and parallel computational models working in a non-synchronized mode, inspired by the mechanism of information processing and communication underlies biological neurons by spikes, where at each computation step, any neuron with applicable rules is not obligatory to exe-cute an applicable rule. It remains an open problem whether AsynSN P systems using stan-dard spiking rules (the execution of the rule only produces a spike) are equivalent in power to Turing machines. In this work, the control mechanism of local synchronization at the rule level is introduced into AsynSN P systems. Namely, there are some given locally syn-chronous sets of rules; if a rule in such set is executed, then all applicable rules residing in the same set should be executed simultaneously. The computational power of AsynSN P systems with local synchronization of rules is examined. It is demonstrated that with local synchronization of rules, both general and unbounded AsynSN P systems are Turing uni-versal, whereas bounded AsynSN P systems can only characterize the family of semilinear sets of numbers, using standard spiking rules. These results demonstrate the great poten-tial for the local synchronization of rules to improve the computational capability of AsynSN P systems.(c) 2021 Elsevier Inc. All rights reserved.

Automated summary

Asynchronous spiking neural P (AsynSN P) systems are distributed and parallel computational models inspired by biological neurons. This study introduces a control mechanism of local synchronization at the rule level and examines the computational power of different systems. The results show that local synchronization of rules can improve the computational capability of the systems.