Representation and classification of switching functions in digital logic design

在设计计算机芯片时，有三个目标是很重要的：更快、更小和需要更少的功率。尝试并达到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。这种技术已被证明可以突出重要的属性，然后可以在设计过程中使用。我的研究涉及使用自相关（AC）变换。 我以前的工作使用这种转换来识别属性，如对称性和不同类型的分解。 我现在打算将布尔逻辑的现有结果（仅限于0和1）扩展到多值逻辑。 将问题视为多值问题通常可以揭示以前未考虑的解决方案。达到这三个目标的另一种方法是将代表计算机电路的功能分类为具有相似属性的组。 我建议在这个应用中也使用AC系数。 初步工作表明，AC系数的使用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。 可逆逻辑的优点是，具有这种特性的电路理论上几乎不需要消耗任何电力。 例如，这意味着手机电池几乎可以永远使用。 然而，我们仍然必须优化面积和速度，并且对于可逆电路，也必须解决上述许多相同的问题。 这个领域是如此的新，以至于诸如如何构建时钟电路和使用已知的工具（如决策图）等问题仍然必须得到回答。 这是我继续研究的一个主要重点。

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.