Representation and classification of switching functions in digital logic design

在设计计算机芯片时，重要的是要瞄准三个目标：速度更快、更小和需要更少的功率。尝试和实现这些目标的一种方法是对函数应用数学变换，并对结果值执行分析。这项技术已被证明可以突出重要的特性，然后可以在设计过程中使用。我的研究涉及到自相关(AC)变换的使用。在我之前的工作中，我使用这种变换来识别对称性和不同类型的分解等性质。我现在打算将现有的结果从仅限于0‘S和1’S的布尔逻辑扩展到多值逻辑。但是，将一个问题视为一个多值问题，往往可以揭示以前没有考虑过的解。实现这三个目标的另一种方法是将代表计算机电路的函数分成具有相似性质的组。我建议在这个应用中也使用交流系数。我的初步工作表明，使用交流系数提供了一种独特的分类技术，这也可以扩展到多值逻辑。另一个研究领域涉及使用一种新型的可逆逻辑电路。可逆逻辑的优势是，用这种性质创造的电路在理论上可以几乎不使用电力！这将意味着，例如，手机电池可以几乎永远使用。然而，我们仍然必须优化面积和速度，许多同样的问题也必须解决可逆电路。这个领域是如此之新，以至于如何构建时钟电路和使用已知的工具，如决策图。这些都是我继续研究的主要重点。

It is important when designing a computer chip to aim for three goals:  faster, smaller, and requiring less power. One way to try and reach these goals is to apply a mathematical transform to the function and perform analysis on the resulting values. This technique has been shown to highlight important properties  that can then be used in the design process. My research involves the use of the autocorrelation (AC) transform.  My previous work used this transform to identify properties such as symmetries and different types of decompositions.  I now intend to extend the existing results from Boolean logic, limited to only 0's and 1's, to multiple-valued logic.  Viewing a problem as a multiple-valued problem can often shed light on previously unconsidered solutions. Another approach for reaching the three goals is to classify the functions representing the computer circuits into groups with similar properties.  I propose to use the AC coefficients in this application as well.  Preliminary work has shown that the use of AC coefficients provides a unique classification technique, and this can also be extended to multiple-valued logic. An additional area of research involves the use of a new type of logic circuit that is reversible.  The advantage of reversible logic is that circuits created with this property can theoretically use almost no power!  This would mean, for instance, that batteries for cell phones could last almost forever.  However, we must still optimize for area and speed and so many of the same questions as above must also be addressed for reversible circuits.  This area is so new that questions such as how to build clocked circuits and use known tools such as decision diagrams still must be answered.  These are a major focus of my continuing research.