In this paper, we present a novel data structure for compact representation and effective manipulations of Boolean functions, called Bi-Kronecker Functional Decision Diagrams (BKFDDs). BKFDDs integrate the classical expansions (the Shannon and Davio expansions) and their bi-versions. Thus, BKFDDs are the generalizations of existing decision diagrams: BDDs, FDDs, KFDDs and BBDDs. Interestingly, under certain conditions, it is sufficient to consider the above expansions (the classical expansions and their bi-versions). By imposing reduction and ordering rules, BKFDDs are compact and canonical forms of Boolean functions. The experimental results demonstrate that BKFDDs outperform other existing decision diagrams in terms of sizes.
Strategy representation and reasoning has recently received much attention in artificial intelligence. Impartial combinatorial games (ICGs) are a type of elementary and fundamental games in game theory. One of the challenging problems of ICGs is to construct winning strategies, particularly, generalized winning strategies for possibly infinitely many instances of ICGs. In this paper, we investigate synthesizing generalized winning strategies for ICGs. To this end, we first propose a logical framework to formalize ICGs based on the linear integer arithmetic fragment of numeric part of PDDL. We then propose an approach to generating the winning formula that exactly captures the states in which the player can force to win. Furthermore, we compute winning strategies for ICGs based on the winning formula. Experimental results on several games demonstrate the effectiveness of our approach.
The movement characteristics that nodes exhibit will bring serious problems in a Wireless Sensor Network (WSN) because most of the protocols do not adapt to node movement. This requires a mobility-aware evaluation technique to locate nodes, forecast communication quality, trace the movement trajectory and formulate thresholds to initiate future handover. One off-the-shelf technology using the Received Signal Strength Indicator (RSSI) of wireless radio is extensively adopted because of the small expense. A node can compute the relative distance between it and its partner by using RSSI readings. However, the measurement results of RSSI fluctuate significantly due to the effects of shadowing and fading. This paper is oriented to investigate the localization accuracy of RSSI in an outdoor ambient condition. To do this, some dynamic and stationary tests are carried out, a calibration line displaying the one-to-one match between RSSI and distance is mapped, five filtering approaches are developed to alleviate the fluctuation of movement curves, and the alleviation effect is measured by calculating the Root Mean Square Error (RMSE) values and by converting the time-domain filtering results into the Fast Fourier Transform (FFT) spectrum. Although the optimized RMSE is reduced to 0.86 and the noise FFT amplitude is less than 1dBm, it may still have a single RSSI value corresponding to more than one distance. Moreover, these distances can differ as much as 2.8m. Since the evaluation error is not acceptable for most cases, it is inaccurate for a mobile node to measure the distance from its partner rely on RSSI readings under outdoor scenarios.
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