Abstract
The number m0 of thresholds is a measure of space complexity, whereas the observation length N is a measure of time complexity that quantifies how fast uncertainty can be reduced. The significance of understanding space and time complexities can be illustrated by the following example. For computer information processing of a continuous-time system, its output must be sampled (e.g., with a sampling rate N Hz) and quantized (e.g., with a precision word-length of B bits). Consequently, its output observations carry the data-flow rate of NB bits per second (bps). For instance, for 8- bit precision and a 10-KHz sampling rate, an 80K-bps bandwidth of data transmission resource is required. In a sensor network in which a large number of sensors must communicate within the network, such resource demand is overwhelming especially when wireless communications of data are involved.
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