This paper is built upon our earlier work on using a Markovian approach to design demodulators for diffusion-based molecular communications. In this earlier work, we show that demodulation can be performed by using a bank of analog filters, which are modelled by ordinary differential equations, to compute the log-posteriori probability that a transmission symbol is transmitted given the observations available to the demodulator. This earlier work was recently extended in two different ways. First, the earlier work assumes that the receiver is limited to a small volume called a voxel. We recently extended the work to the case where a receiver is modelled by a volume consisting of multiple voxels. In particular, we show that we can reduce the bit error rate by using receivers that are spatially partitioned. Second, the earlier work assumes that the computation of the log-posteriori probability is carried out in silico. We recently showed how the computation can be approximately carried out by a molecular circuit, i.e. a set of reactions. This paper builds on these two recent extensions. We make the following contributions. First, we derive molecular circuits to approximately compute the log-posteriori probability for partitioned receivers. We show how this is done for two different types of concentration modulation schemes. Second, the earlier work considered the demodulation of only one symbol. We extend the work so that the demodulator can decode a sequence of symbols by introducing a reset mechanism in the demodulator.