Inversion optimization in majority inverter graph with minority operations : A novel approach

Abstract

On account of their simplicity, homogeneous logic representations have drawn attention in the domain of logic synthesis. In such representations, combinational circuits are often modeled as Directed Acyclic Graph (DAG) wherein terminal nodes represent primary inputs and other nodes represent same Boolean logic operation. The edges in DAGs can be complemented where the nodes have a complemented output, which renders a functionally universal representation. Such homogeneous logic representations simplify optimization algorithms significantly, hence, assist in e⇥cient implementation. This thesis performs an analysis into the inversion optimization of a homogeneous logic representation, referred to as majority inverter graph (MIG) using minority operations. MIG is a logic representation structure that along with its algebraic properties and Boolean transformation methods synthesizes circuits with significant optimization in terms of size, depth, and switching activity. In this work, we first propose rules and properties for logic representations with minority and inversion operations referred to as mIG logic synthesis. Subsequently, we propose synthesis techniques based on minority, majority, and inversion operations, referred to as mMIG synthesis. We propose an algorithm based on the rules and properties to achieve an optimization in terms of area reduction and inversion reduction in mMIG-based circuit synthesis. We present comparison of resource consumption in mMIG logic synthesis with existing MIG synthesis techniques, and present some important observations towards inverter optimization. These propsed methods have been tested on various standard benchmark circuits, such as EPFL benchmark suites, ISCAS’85 and also on lightweight cryptographic block ciphers and cryptoprimitives. Analysis of the implementation results demonstrates that the proposed mMIG structure outperforms the existing MIG structure mainly in term of reduction in inversion count which can have major impact in emerging technologies such as quantum dot cellular automata (QCA) and spin wave devices (SWDs), and inversion intensive circuits such as RAM address-decoding circuits. Keywords: Minority logic, Inversion, Boolean algebra, Majority logic, Inversion Optimization