Formal verification of energy consumption for an EEG monitoring wireless body area sensor network

Wireless Body Area Sensor Networks (BASNs) are increasingly gaining notable attention in the domain of real-time and non-invasive human health care due to their cost-effectiveness. Minimizing their energy consumption under given data delay and distortion constraints is considered to be the most critical design factor for BASNs and specialized algorithms are developed for finding optimal parameters for minimizing the energy levels for BASNs. The optimization criteria are usually obtained based on the energy, delay and distortion relationships for the given BASN using paper-and-pencil proof and the performance of optimal parameter-finding algorithms is usually analyzed using simulation techniques. Due to the informal nature of paper-and-pencil proofs and simulation, 100% accuracy can never be ascertained, which is a severe limitation considering the safety-critical nature of BASNs. To overcome this limitation, we propose to use higher-order-logic theorem proving to conduct these analyses. As a first step towards this direction, this paper presents the higher-order-logic formalization of the commonly used mathematical relationships for energy consumption, data delay deadlines and distortion threshold constraints for an EEG monitoring BASN. These relationships can in turn be used for devising the optimization problem for the given BASN configuration.