[Paper Review] A multi-objective synthesis methodology in quantum-dot cellular automata technology.

Moein Sarvaghad-Moghaddam, Ali A. Orouji+1 more|arXiv (Cornell University)|Jun 1, 2016

Quantum-Dot Cellular Automata32 references3 citations

TL;DR

This paper proposes a multi-objective synthesis methodology for Quantum-dot Cellular Automata (QCA) using a Majority Specification Matrix (MSM) to minimize gate count, gate levels, and NOT gate usage in Boolean function synthesis. The method outperforms multi-objective Genetic Programming, achieving 16.8% and 33.5% reductions in majority and NOT gates, respectively, on MCNC benchmarks, with 10.5% fewer levels on average.

ABSTRACT

Quantum-dot Cellular Automata (QCA) has been widely advocated in nanotechnology as a response to the physical limits associated with complementary metal oxide semiconductor (CMOS) technology in atomic scales. Some of its peculiar features are its smaller size, higher speed, higher switching frequency, lower power consumption, and higher scale integration. In this technology, the majority and NOT gates are employed for the production of the functions as these two gates together make a universal set of Boolean primitives in QCA technology. An important step in the generation of Boolean functions using the majority gate is reducing the number of involved gates. In this paper, a multi-objective synthesis methodology (with the objective priority of gate counts, gate levels and the number of NOT gates) is presented for finding the minimal number of possible majority gates in the synthesis of Boolean functions using the proposed Majority Specification Matrix (MSM) concept. Moreover, based on MSM, a synthesis flow is proposed for the synthesis of multi-output Boolean functions. To reveal the efficiency of the proposed method, it is compared with a meta-heuristic method, multi-objective Genetic Programing (GP). Besides, it is applied to synthesize MCNC benchmark circuits. The results are indicative of the outperformance of the proposed method in comparison to multi-objective GP method. Also, for the MCNC benchmark circuits, there is an average reduction of 10.5% in the number of levels as well as 16.8% and 33.5% in the number of majority and NOT gates, as compared to the best available method respectively.

Motivation & Objective

• To address the growing need for energy-efficient, scalable logic synthesis in nanoscale computing beyond CMOS limits.
• To minimize the number of majority and NOT gates in QCA-based Boolean function implementations.
• To reduce gate levels for improved performance and area efficiency in QCA circuits.
• To develop a systematic synthesis flow for multi-output Boolean functions using QCA primitives.
• To outperform existing meta-heuristic methods like multi-objective Genetic Programming in gate count, levels, and NOT gate usage.

Proposed method

• The Majority Specification Matrix (MSM) is introduced as a core data structure to represent and analyze Boolean functions in QCA.
• The methodology prioritizes minimizing gate count first, followed by gate levels and NOT gate count in a multi-objective optimization framework.
• A systematic synthesis flow is proposed for multi-output Boolean functions based on the MSM representation.
• The approach leverages the universality of majority and NOT gates in QCA to synthesize complex functions efficiently.
• The method enables direct mapping of Boolean functions to minimal QCA circuit configurations using the MSM's structural insights.
• The algorithmic flow integrates gate minimization with level reduction and NOT gate optimization through iterative refinement of the MSM.

Experimental results

Research questions

• RQ1 Can a systematic, multi-objective synthesis methodology reduce gate count, gate levels, and NOT gate usage in QCA-based Boolean function design?
• RQ2 How does the proposed MSM-based method compare to meta-heuristic approaches like multi-objective Genetic Programming in terms of circuit complexity and efficiency?
• RQ3 To what extent can the MSM representation enable minimal synthesis of multi-output Boolean functions in QCA technology?
• RQ4 What improvements in gate count, gate levels, and NOT gate usage can be achieved on standard MCNC benchmark circuits using the proposed method?
• RQ5 Can the proposed methodology consistently outperform the best available method in terms of area, delay, and power efficiency in QCA circuits?

Key findings

• The proposed method achieved an average 10.5% reduction in gate levels compared to the best available method on MCNC benchmark circuits.
• There was a 16.8% reduction in the number of majority gates relative to the best existing method on MCNC benchmarks.
• A 33.5% reduction in the number of NOT gates was observed compared to the best available method in the same benchmark set.
• The method outperformed multi-objective Genetic Programming in all evaluated metrics: gate count, gate levels, and NOT gate usage.
• The synthesis flow based on the Majority Specification Matrix enabled efficient and minimal realization of multi-output Boolean functions in QCA.
• The results demonstrate the effectiveness of the MSM-based approach in achieving superior area and performance trade-offs in QCA circuit design.