In this paper are given two novel algorithms for minimization of recursive Boolean formula (RBF), which is adequate for implementation of N-input 1-output Boolean functions (BFs) over basis {imply, false} using two memristors. Both of our algorithms are direct consequence of necessary and sufficient conditions related to regular ordering of positive product terms within recursive formula. The results demonstrate how developed algorithms provide up to 26% gain in average number of implications and shorter recursive Boolean formula length in up to 77% of problem instances than previously published algorithms, tested on the set of all 4-input 1-output BFs.

In this paper, we used the accepted methodology of applying probabilistic-model checking to dynamic power management. For the first time, we analyze in this context a dynamic-power-management system with the two request priorities. First system we consider has a single two-priority service request queue. Second system to be analyzed has two single service request queues that are dedicated for high- and low-priority requests. We calculate optimal stochastic policies for the both systems. The same delay constraint is applied on the whole queue of the first system and on the high-priority (QH) queue of the second system. The comparison of the power consumptions of the two systems shows that the second system consumes up to 77% less power. We obtain that the power consumptions of both systems converge when the constraints become tighter. We demonstrate that, with the increased length of the QH service request queue of the second system, more power can be saved in applications with varying quality-of-service requirements. Our models and experiments can be easily generalized toNrequest priorities and different queue lengths.