In this paper, we propose a paradigm shift in representing and optimizing logic by using only majority (MAJ) and inversion (INV) functions as basic operations. We represent logic functions by Majority-Inverter Graph (MIG): a directed acyclic graph consisting of three-input majority nodes and regular/complemented edges. We optimize MIGs via a new Boolean algebra, based exclusively on majority and inversion operations, that we formally axiomatize in this work. As a complement to MIG algebraic optimization, we develop powerful Boolean methods exploiting global properties of MIGs, such as bit-error masking. MIG algebraic and Boolean methods together attain very high optimization quality. Considering the set of IWLS'05 benchmarks, our MIG optimizer (MIGhty) enables a 7% depth reduction in LUT-6 circuits mapped by ABC while also reducing size and power activity, with respect to similar AIG optimization. Focusing on arithmetic intensive benchmarks instead, MIGhty enables a 16% depth reduction in LUT-6 circuits mapped by ABC, again with respect to similar AIG optimization. Employed as front-end to a delay-critical 22-nm ASIC flow (logic synthesis + physical design) MIGhty reduces the average delay/area/power by 13%/4%/3%, respectively, over 31 academic and industrial benchmarks. We also demonstrate delay/area/power improvements by 10%/10%/5% for a commercial FPGA flow.

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Abstract-We present a novel class of decision diagrams, called Biconditional Binary Decision Diagrams (BBDDs), that enable efficient logic synthesis for XOR-rich circuits. BBDDs are binary decision diagrams where the Shannon's expansion is replaced by the biconditional expansion. Since the biconditional expansion is based on the XOR/XNOR operations, XOR-rich logic circuits are efficiently represented and manipulated with canonical Reduced and Ordered BBDDs (ROBBDDs). Experimental results show that ROBBDDs have 37% fewer nodes on average compared to traditional ROBDDs. To exploit this opportunity in logic synthesis for XOR-rich circuits, we developed a BBDD-based One-Pass Synthesis (OPS) methodology. The BBDD-based OPS is capable to harness the potential of novel XOR-efficient devices, such as ambipolar transistors. Experimental results show that our logic synthesis methodology reduces the number of ambipolar transistors by 49.7% on average with respect to stateof-art commercial logic synthesis tool. Considering CMOS technology, the BBBD-based OPS reduces the device count by 31.5% on average compared to commercial synthesis tool.

Abstract-In this paper, we present a design and benchmarking methodology of Spin Wave Device (SWD) circuits based on micromagnetic modeling. SWD technology is compared against a 10nm FinFET CMOS technology, considering the key metrics of area, delay and power. We show that SWD circuits outperform the 10nm CMOS FinFET equivalents by a large margin. The areadelay-power product (ADPP) of SWD is smaller than CMOS for all benchmarks from 2.5× to 800×. On average, the area of SWD circuits is 3.5× smaller and the power consumption is two orders of magnitude lower compared to the 10nm CMOS reference circuits.