Grant: Discovery Grants Program - Individual

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.