CSE Technical Reports Sorted by Technical Report Number
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| We define functional abstraction as the process of deliberately ignoring the dependence of a Boolean function on a subset of its variables. Functional abstraction causes a completely specified function to become partially specified. We propose functions sets as a theoretical model for partially specified functions and function intervals as a practical approximation to them. We develop an interval Boolean algebra suitable for the symbolic manipulation of function intervals and highlight the relationship between functional abstraction and universal and existential quantification. |
| While delay modeling of gates with a single switching input has received a lot of attention, the case of multiple inputs switching in close temporal proximity is just beginning to be addressed in the literature. The effect of proximity of input transitions can be significant on the delay and output transition time. The few attempts that have addressed this issue are based on a series-parallel transistor collapsing method that reduces the multi-input gate to an inverter. This limits the technique to CMOS technology. Moreover, none of them discuss the appropriate choice of voltage thresholds to measure delay for a multi-input gate. In this paper, we first present a method for the choice of voltage thresholds for a multi-input gate that ensures a positive value of delay for any combination of input transition times and the temporal separations among them. We next introduce a dual-input proximity model for the case when only two inputs of the gate are switching. We then prose a simple algorithm for calculating the delay and output transition time that makes repeated use of the dual-input proximity model and that does not collapse the gate into a equivalent inverter. Comparison with simulation results shows that our method performs quite well in practice. Before concluding the paper we also show the close relationship between the inertial delay of a gate and the proximity of input transitions. |
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