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、功耗更低。尝试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。这种技术已经被证明可以突出显示在设计过程中可以使用的重要属性。我的研究涉及到使用自相关（AC）变换。我以前的工作使用这种转换来识别对称性和不同类型的分解等属性。我现在打算将现有的结果从布尔逻辑（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。实现这三个目标的另一种方法是将表示计算机电路的函数分类为具有相似属性的组。我建议在这个应用程序中也使用AC系数。初步的工作表明，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一种新型可逆逻辑电路的使用。可逆逻辑的优点是，用这种特性创建的电路理论上几乎不使用电源！例如，这将意味着，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，因此许多相同的问题也必须解决可逆电路。这是一个全新的领域，诸如如何构建时钟电路和使用决策图等已知工具等问题仍有待解决。这是我继续研究的一个主要焦点。

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.