I am a Ph.D. candidate in the Dept. of Electrical and Computer Engineering at the University of Minnesota, Twin Cities Campus.
I am pursuing research on computing models for emerging technologies. I also have a particular interest in combinatorics, more specifically hypergraphs.
In his seminal Master's Thesis, Claude Shannon made the connection between Boolean algebra and switching circuits. He considered two-terminal switches corresponding to electromagnetic relays. A Boolean function can be implemented in terms of connectivity across a network of switches, often arranged in a series/parallel configuration. We have developed a method for synthesizing Boolean functions with networks of four-terminal switches. Our model is applicable for variety of nanoscale technologies, such as nanowire crossbar arrays, as molecular switch-based structures.
Shannon's model: two-terminal switches
. Each switch is either ON (closed) or OFF (open). A Boolean function is implemented in terms of connectivity across a network of switches, arranged in a series/parallel configuration. This network implements the function .
Our model: four-terminal switches
. Each switch is either mutually connected to its neighbors (ON) or disconnected (OFF). A Boolean function is implemented in terms of connectivity between the top and bottom plates. This network implements the same function, .
Percolation for Robust Computation
We have devised a novel framework for digital computation with lattices of nanoscale switches with high defect rates, based on the mathematical phenomenon of percolation. With random connectivity, percolation gives rise to a sharp non-linearity in the probability of global connectivity as a function of the probability of local connectivity. This phenomenon is exploited to compute Boolean functions robustly, in the presence of defects.
In a switching network with defects, percolation can be exploited to produce robust Boolean functionality. Unless the defect rate exceeds an error margin, with high probability no connection forms between the top and bottom plates for logical zero ("OFF"); with high probability, a connection forms for logical one ("ON").
The problem of testing whether a monotone Boolean function in irredundant disjuntive normal form (IDNF) is self-dual is one of few problems in circuit complexity whose precise tractability status is unknown. We have focused on this famous problem. We have shown that monotone self-dual Boolean functions in IDNF do not have more variables than disjuncts. We have proposed an algorithm to test whether a monotone Boolean function in IDNF with n variables and n disjuncts is self-dual. The algorithm runs in time.
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