Abstract — We propose an algorithm for efficient threshold network synthesis of arbitrary multi-output Boolean functions. Many nanotechnologies, such as resonant tunneling diodes (RTDs), quantum cellular automata (QCA), and single electron tunneling (SET), are capable of implementing threshold logic efficiently. The main purpose of this work is to bridge the current wide gap between research on nanoscale devices and research on synthesis methodologies for generating optimized networks utilizing these devices. While functionally-correct threshold gates and circuits based on nanotechnologies have been successfully demonstrated, there exists no methodology or design automation tool for general multi-level threshold network synthesis. We have built the first such tool, ThrEshold Logic Synthesizer (TELS), on top of an existing Boolean logic synthesis tool. Experiments with 56 multioutput benchmarks indicate that, compared to traditional logic synthesis, upto 80.0 % and 70.6 % reduction in gate count and interconnect count, respectively, is possible with the average being 22.7 % and 12.6%, respectively. Furthermore, the synthesized networks are well-balanced structurally. The novelty of this work lies in the introduction of the first comprehensive synthesis methodology and tool for general multi-level threshold logic design. Index Terms — Design automation, logic synthesis, QCA, RTD, threshold networks.

We propose an algorithm for efficient threshold network synthesis of arbitrary multi-output Boolean functions. The main purpose of this work is to bridge the wide gap that currently exists between research on the development of nanoscale devices and research on the development of synthesis methodologies to generate optimized networks utilizing these devices. Many nanotechnologies, such as resonant tunneling diodes (RTD) and quantum cellular automata (QCA), are capable of implementing threshold logic. While functionally correct threshold gates have been successfully demonstrated, there exists no methodology or design automation tool for general multi-level threshold network synthesis. We have built the first such tool, ThrEshold Logic Synthesizer (TELS), on top of an existing Boolean logic synthesis tool. Experiments with about 60 multi-output benchmarks were performed, though the results of only 10 of them are reported in this paper because of space restrictions. They indicate that up to 77% reduction in gate count is possible when utilizing threshold logic, with an average reduction being 52%, compared to traditional logic synthesis. Furthermore, the synthesized networks are well-balanced, and hence delay-optimized.

This paper gives a brief account of the results on hardware implementations of threshold logic obtained starting from the forties. The solutions are sorted chronologically, by order of their publication date, although the order would be somehow different by submission date. Reviewing the many different solutions, we will identify those that have been enduring, and mention a few that have been long forgotten, but rediscovered a few decades later.

Power constrained systems, di erent from traditional low power systems, are becoming more recognized. The operation of these systems is not constrained only by the availability of traditional resources such as software or hardware, but is limited by applicable power. Designing such systems poses new challenges. We meet these challenges by departing from the classical low power design approach and taking a power elastic system view. In this paper we present an architectural level solution based on real-time feedback control to t system operation into power constraint pro les. Investigations into concurrency management as the main method for such real-time control are carried out. As part of this methodology we present a new approach, called `soft arbitration', which can be applied to solving the problem of energy resource allocation and power capping. This work provides a concrete foundation for the power elastic methodology through developing a set of modelling, analysis, design and implementation techniques covering both theoretical and practical issues. 1

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