Related papers: Multi-output, multi-level, multi-gate design using…
New technologies such as Quantum-dot Cellular Automata (QCA), Single Electron Tunneling (SET), Tunneling Phase Logic (TPL) and all-spin logic (ASL) devices have been widely advocated in nanotechnology as a response to the physical limits…
We consider the multiplicative complexity of Boolean functions with multiple bits of output, studying how large a multiplicative complexity is necessary and sufficient to provide a desired nonlinearity. For so-called $\Sigma\Pi\Sigma$…
The construction of quantum computers is based on the synthesis of low-cost quantum circuits. The quantum circuit of any Boolean function expressed in a Positive Polarity Reed-Muller $PPRM$ expansion can be synthesized using…
A notorious open question in circuit complexity is whether Boolean operations of arbitrary arity can efficiently be expressed using modular counting gates only. H{\aa}stad's celebrated switching lemma yields exponential lower bounds for the…
Noise-based logic, by utilizing its multidimensional logic hyperspace, has significant potential for low-power parallel operations in beyond-Moore-chips. However universal gates for Boolean logic thus far had to rely on either time…
The physical limitations of CMOS technology triggered several research for finding an alternative technology. QCA is one of the emerging nanotechnologies which is gaining attention as a substitute of CMOS. The main potential of QCA is its…
Invertible logic can operate in one of two modes: 1) a forward mode, in which inputs are presented and a single, correct output is produced, and 2) a reverse mode, in which the output is fixed and the inputs take on values consistent with…
We present a constructive SAT-based algorithm to determine the multiplicative complexity of a Boolean function, i.e., the smallest number of AND gates in any logic network that consists of 2-input AND gates, 2-input XOR gates, and…
We present a general method for analysing novel computational substrates to determine which of their parameters can be manipulated to exhibit the complete set of 2-input boolean logical operations. We demonstrate this approach with an…
Quantum Hamiltonian Computing is a recent approach that uses quantum systems, in particular a single molecule, to perform computational tasks. Within this approach, we present explicit methods to construct logic gates using two different…
A monotone Boolean circuit is composed of OR gates, AND gates and input gates corresponding to the input variables and the Boolean constants. It is $q$-multilinear if for each its output gate $o$ and for each prime implicant $s$ of the…
We consider boolean circuits computing n-operators f:{0,1}^n --> {0,1}^n. As gates we allow arbitrary boolean functions; neither fanin nor fanout of gates is restricted. An operator is linear if it computes n linear forms, that is, computes…
Polynomial threshold gates are basic processing units of an artificial neural network. When the input vectors are binary vectors, these gates correspond to Boolean functions and can be analyzed via their polynomial representations. In…
Gate-model quantum computers provide an experimentally implementable architecture for near term quantum computations. To design a reduced quantum circuit that can simulate a high complexity reference quantum circuit, an optimization should…
We construct logical gates via topology optimisation (aimed to solve a station problem of heat conduction) of a conductive material layout. Values of logical variables are represented high and low values of a temperature at given sites.…
Multi-valued logic gates, which can handle quaternary numbers as inputs, are developed by exploiting the ballistic transport properties of quantum point contacts in series. The principle of a logic gate that finds the minimum of two…
Two-level logic minimization is a central problem in logic synthesis, and has applications in reliability analysis and automated reasoning. This paper represents a method of minimizing Boolean sum of products function with binary decision…
Towards better understanding of gate elimination, the only method known that can prove complexity lower bounds for explicit functions against unrestricted Boolean circuits, this work contributes: (1) formalizing circuit simplifications as a…
A long-standing goal of computer technology is to process and store digital information with the same device in order to implement new architectures. One way to accomplish this is to use nanomagnetic `non-volatile' logic gates that can…
We develop a multi-valued logic for quantum computing for use in multi-level quantum systems, and discuss the practical advantages of this approach for scaling up a quantum computer. Generalizing the methods of binary quantum logic, we…