Reversible logic circuit is a necessary construction for achieving ultra low power dissipation as well as for prominent post-CMOS computing technologies such as Quantum computing. Consequently automatic synthesis of a Boolean function using elementary reversible logic gates has received significant research attention in recent times, creating the domain of reversible logic synthesis. In this pa...

In the modern digital system design the reliability and security of memories are essential considerations. As technology scales, memory devices become larger and more powerful error correction codes are needed to protect memories from soft errors. Low Density Parity Check (LDPC) Codes are the class of linear block codes which provide near capacity performance on large collection of data transmi...

A low-density parity-check (LDPC) code is a linear error correcting code, and is used for transmitting message over a noisy transmission channel. A new class of error correcting codes called EG-LDPC (Euclidean Geometry-LDPC) codes and its encoder and decoder architectures for nanomemory applications is designed. EG-LDPC codes also have fault secure detection capability. One step majority logic ...

We describe the operation of, and demonstrate logic functionality in, networks of physically coupled, nanometer-scale magnets designed for digital computation in magnetic quantum-dot cellular automata (MQCA) systems. MQCA offer low power dissipation and high integration density of functional elements and operate at room temperature. The basic MQCA logic gate, that is, the three-input majority l...

Reversible logic synthesis is emerging as a major research component for post-CMOS computing devices, in particular Quantum computing. In this work, we link the reversible logic synthesis problem to sorting algorithms. Based on our analysis, an alternative derivation of the worst-case complexity of generated reversible circuits is provided. Furthermore, a novel column-wise reversible logic synt...

In the first part of this lecture, we analyze the noise sensitivity of the Majority function in more detail than last time. In the second part, we discuss the Majority is Stablest theorem, which says that among balanced functions for which each of the individual variables has low influence, the Majority function has the lowest noise sensitivity up to some small error. We also see some applicati...

Abstract Predicate intuitionistic logic is a well-established fragment of dependent types. Proof construction in this logic, as the Curry–Howard isomorphism states, process program synthesis. We present automata that can handle proof and synthesis full first-order logic. Given formula, we construct an automaton such formula provable if only has accepting run. As further research, makes it possi...

We present introductory considerations and analysis toward computing applications based on the recently introduced deterministic logic scheme with random spike (pulse) trains [Phys. Lett. A 373 (2009) 2338–2342]. Also, in considering the questions, “why random?” and “why pulses?”, we show that the random pulse based scheme provides the advantages of realizing multivalued deterministic logic. Pu...