Research
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| − | || [[Image:4-switch.png|center|thumb|none|375px|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, f = x_1 x_2 x_3 + x_1 x _2 x_5 x_6 + x_4 x_5 x_2 x_3 + x_4 | + | || [[Image:4-switch.png|center|thumb|none|375px|link=|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, f = x_1 x_2 x_3 + x_1 x _2 x_5 x_6 + x_4 x_5 x_2 x_3 + x_4 |
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We have devised a novel framework for digital computation with lattices of nanoscale switches with high defect rates, based on the mathematical phenomenon of [http://en.wikipedia.org/wiki/Percolation_theory 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. | We have devised a novel framework for digital computation with lattices of nanoscale switches with high defect rates, based on the mathematical phenomenon of [http://en.wikipedia.org/wiki/Percolation_theory 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. | ||
| − | [[Image:Lattice-defects-percolation.jpg|left|thumb|none|900px|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").]] | + | [[Image:Lattice-defects-percolation.jpg|left|thumb|none|900px|link=|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").]] |
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Revision as of 22:39, 26 October 2013
Our research is multidisciplinary and spans areas such as circuit design, emerging computing models, and mathematics. Our main goal is developing novel ways of computing for nanoscale technologies.
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Computing with Networks of Nanoswitches
As current CMOS-based technology is approaching its anticipated limits, research is shifting to novel forms of nanoscale technologies including molecular-scale self-assembled systems. Unlike conventional CMOS that can be patterned in complex ways with lithography, self-assembled nanoscale systems generally consist of regular structures. Logical functions are achieved with crossbar-type switches. Our model, a network of four- terminal switches, corresponds to this type of switch in a variety of emerging technologies, including nanowire crossbar arrays and magnetic switch-based structures.
Synthesis Problem
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, arranged in rectangular lattices.
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File:2-switch.png 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 f = x_1 x_2 x_3 + x_1 x _2 x_5 x_6 + x_4 x_5 x_2 x_3 + x_4 x_5 x_6. |
File:4-switch.png 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, f = x_1 x_2 x_3 + x_1 x _2 x_5 x_6 + x_4 x_5 x_2 x_3 + x_4 x_5 x_6. |
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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.
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Mathematics
Self-Duality Problem
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 O(n^4) time.
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Analog Circuit Design
Positive Feedback
The conventional wisdom is that analog circuits should not include positive feedback loops. As controversial as it seems, we have successfully used positive feedback for impedance improvement in a current amplifier. With adding few transistors we have achieved very low input resistance values. We have tested the proposed fully-differential current amplifier in a filter application.
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