Biocomputing technologies exploit biological communication mechanisms involving cell-cell signal propagation to perform computations. Researchers recently worked toward realising logic gates made by neurons to develop novel devices such as organic neuroprostheses or brain implants made by cells, herein termed living implants. Several challenges arise from this approach, mainly associated with the stochastic nature and noise of neuronal communication. Since astrocytes play a crucial role in the regulation of neurons activity, there is a possibility whereby astrocytes can be engineered to control synapses favouring reliable biocomputing. This work proposes a mathematical model of neuronal logic gates involving neurons and astrocytes, realising OR and AND gating. We use a shallow coupling of both the Izhikevich and Postnov models to characterise gating responses with spike pattern variability and astrocyte synaptic regulation. Logic operation error ratio and accuracy assess the AND and OR gates' performances at different synaptic Gaussian noise levels. Our results demonstrate that the astrocyte regulating activity can effectively be used as a denoising mechanism, paving the way for highly reliable biocomputing implementations.