Logic resynthesis is one of the core problems in modern peephole logic optimization algorithms. Given a target function and set existing functions, asks for circuit reusing some functions generating target. While exact methods such as enumeration SATbased synthesis guarantee optimal solutions, limitations on problem size are inevitable due to scalability concerns. In this work, we propose heuri...

Individual transistors based on emerging reconfigurable nanotechnologies exhibit electrical conduction for both types of charge carriers. These [referred to as field-effect (RFETs)] enable dynamic reconfiguration demonstrate either a p- or an n-type functionality. This duality functionality at the transistor level is efficiently abstracted self-dual Boolean logic, that can be physically realize...

We investigate the benefit of using ESOP minimization in the synthesis of quantum-dot cellular automata (QCA). We determine the size and delay of multi-input XOR and AND/OR gates when implemented in using 3-input majority gates that are easily realized in QCA, and use our results in our QCAexor estimator tool. We found that most benchmarks have at least one output that can be better minimized u...

In this article, we consider Schubert codes, linear codes associated to varieties, and discuss minimum weight codewords for dual codes. The notion of lines in varieties is looked closely at, it has been proved that the supports lie on any three points a line variety correspond support some parity check code. We use these construct orthogonal checks certain them majority logic decoding. special ...

Most logic synthesis algorithms work on graph representations of functions with nodes associated arbitrary expressions or simple and iteratively optimize such graphs. While recent multilevel efforts focused primarily graphs 2-input as AND OR gates, the recently proposed paradigm Majority-Inverter Graphs (MIGs) instead uses 3-input Majority gate node function. As this technique proved to be a su...

In this article, we consider the decoding problem of Grassmann codes using majority logic. We show that for two points Grassmannian, there exists a canonical geodesic between these once complete flag is fixed. These geodesics are used to construct large set parity checks orthogonal on coordinate code, resulting in algorithm.