Related papers: Logical N-AND Gate on a Molecular Turing Machine
Logic Programming languages and combinational circuit synthesis tools share a common "combinatorial search over logic formulae" background. This paper attempts to reconnect the two fields with a fresh look at Prolog encodings for the…
We put forward a new proposal of designing charge-based logic devices considering a cyclic molecule that can be programmed and re-programmed for different functional logical operations and suitably engineered for data storage as well. The…
We derive an encoded universality representation for a generalized anisotropic exchange Hamiltonian that contains cross-product terms in addition to the usual two-particle exchange terms. The recently developed algebraic approach is used to…
Theoretical constructs of logical gates implemented with plant roots are morphological computing asynchronous devices. Values of Boolean variables are represented by plant roots. A presence of a plant root at a given site symbolises the…
We give several different encodings of the step function of a Turing machine in intuitionistic linear logic, and calculate the denotations of these encodings in the Sweedler semantics.
This paper expresses the structure of artificial neural network (ANN) as a functional form, using the activation integral concept derived from the activation function. In this way, the structure of ANN can be represented by a simple…
Quantum error correcting codes protect quantum computation from errors caused by decoherence and other noise. Here we study the problem of designing logical operations for quantum error correcting codes. We present an automated procedure…
Based on the concept of DNA strand displacement and DNA strand algebra we have developed a method for logical inference which is not based on silicon based computing. Essentially, it is a paradigm shift from silicon to carbon. In this paper…
Boolean algebra, the branch of mathematics where variables can assume only true or false value, is the theoretical basis of classical computation. The analogy between Boolean operations and electronic switching circuits, highlighted by…
The molecular computing has been successfully employed to solve more and more complex computation problems. However, as an important complex problem, the model checking are still far from fully resolved under the circumstance of molecular…
Is there any hope for quantum computing to challenge the Turing barrier, i.e. to solve an undecidable problem, to compute an uncomputable function? According to Feynman's '82 argument, the answer is {\it negative}. This paper re-opens the…
Junctionless oxide-based neuron thin-film transistors with in-plane-gate structure are fabricated at room temperature with a laser scribing process. The neuron transistors are composed of a bottom ITO floating gate and multiples of two…
Providing explanations for the outputs of artificial neural networks (ANNs) is crucial in many contexts, such as critical systems, data protection laws and handling adversarial examples. Logic-based methods can offer explanations with…
Turing machines and register machines have been used for decades in theoretical computer science as abstract models of computation. Also the $\lambda$-calculus has played a central role in this domain as it allows to focus on the notion of…
We show how to perform a fault-tolerant universal quantum computation in 2D architectures using only transversal unitary operators and local syndrome measurements. Our approach is based on a doubled version of the 2D color code. It enables…
Ternary logic is expected to increase the area efficiency of VLSI due to its expressiveness compared to the traditional binary logic. This paper proposes a new symmetric ternary logic and a systematic logic composition methodology that…
We design a proof system for propositional classical logic that integrates two languages for Boolean functions: standard conjunction-disjunction-negation and binary decision trees. We give two reasons to do so. The first is…
Logical relations widely exist in human activities. Human use them for making judgement and decision according to various conditions, which are embodied in the form of \emph{if-then} rules. As an important kind of cognitive intelligence, it…
Entanglement is a physical phenomenon, which has fueled recent successes of quantum algorithms. Although quantum neural networks (QNNs) have shown promising results in solving simple machine learning tasks recently, for the time being, the…
Boolean functions have important applications in cryptography and coding theory. Two famous classes of binary codes derived from Boolean functions are the Reed-Muller codes and Kerdock codes. In the past two decades, a lot of progress on…