Related papers: Logical N-AND Gate on a Molecular Turing Machine

Logic locking aims to prevent intellectual property (IP) piracy and unauthorized overproduction of integrated circuits (ICs). However, initial logic locking techniques were vulnerable to the Boolean satisfiability (SAT)-based attacks. In…

Currently, there is a lack of rigorous theoretical system for systematically generating non-trivial and logically valid theorems. Addressing this critical gap, this paper conducts research to propose a novel automated theorem generation…

Landauer's principle places a fundamental lower limit on the work required to perform a logically irreversible operation. Logically reversible gates provide a way to avoid these work costs, and also simplify the task of making the…

{\em Computability logic} (CoL) is a powerful, mathematically rigorous computational model. In this paper, we show that CoL-web, a web extension to CoL, naturally supports web programming where database updates are involved. To be specific,…

In this paper, we explore the interaction between two monoidal structures: a multiplicative one, for the encoding of pairing, and an additive one, for the encoding of choice. We propose a colored PROP to model computation in this framework,…

A global race towards developing a gate-based, universal quantum computer that one day promises to unlock the never before seen computational power has begun and the biggest challenge in achieving this goal arguably is the quality…

A numeral system is an infinite sequence of different closed normal $\lambda$-terms intended to code the integers in $\lambda$-calculus. H. Barendregt has shown that if we can represent, for a numeral system, the functions : Successor,…

The extent to which neural networks are able to acquire and represent symbolic rules remains a key topic of research and debate. Much current work focuses on the impressive capabilities of large language models, as well as their often…

In this paper, we study the complexity of evaluating Conjunctive Queries with negation (\cqneg). First, we present an algorithm with linear preprocessing time and constant delay enumeration for a class of CQs with negation called…

Short-circuit evaluation denotes the semantics of propositional connectives in which the second argument is evaluated only if the first argument does not suffice to determine the value of the expression. In programming, short-circuit…

Although the initial proposal for ion trap quantum computation made use of an auxiliary internal level to perform logic between ions, this resource is not necessary in principle. Instead, one may perform such operations directly using…

Boolean function bi-decomposition is ubiquitous in logic synthesis. It entails the decomposition of a Boolean function using two-input simple logic gates. Existing solutions for bi-decomposition are often based on BDDs and, more recently,…

Atomic-scale logic and the minimization of heating (dissipation) are both very high on the agenda for future computation hardware. An approach to achieve these would be to replace networks of transistors directly by classical reversible…

Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html ) is a research program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth which it has more traditionally been.…

The model theory of a first-order logic called N^4 is introduced. N^4 does not eliminate double negations, as classical logic does, but instead reduces fourfold negations. N^4 is very close to classical logic: N^4 has two truth values;…

One of the possible representations of three-valued instantaneous noise-based logic is proposed. The third value is an uncertain bit value, which can be useful in artificial intelligence applications. There is a forth value, too, that can…

Following the success of Moore's predictions, we are approaching a limit in the miniaturization of semiconductors for computing materials. This has led to the exploration of various research paths to develop alternative computing paradigms,…

We consider an old question of Slaman and Steel: whether Turing equivalence is an increasing union of Borel equivalence relations none of which contain a uniformly computable infinite sequence. We show this question is deeply connected to…

Neural networks, as currently designed, fall short of achieving true logical intelligence. Modern AI models rely on standard neural computation-inner-product-based transformations and nonlinear activations-to approximate patterns from data.…

DNA has been discussed as a potential medium for data storage. Potentially it could be denser, could consume less energy, and could be more durable than conventional storage media such as hard drives, solid-state storage, and optical media.…