Related papers: A Short Note on Improved Logic Circuits in a Hexag…

Proving complexity lower bounds remains a challenging task: we only know how to prove conditional uniform lower bounds and nonuniform lower bounds in restricted circuit models. Williams (STOC 2010) showed how to derive nonuniform lower…

This note is concerned with a formal analysis of the problem of non-monotonic reasoning in intelligent systems, especially when the uncertainty is taken into account in a quantitative way. A firm connection between logic and probability is…

Theoretical computer scientists have been debating the role of oracles since the 1970's. This paper illustrates both that oracles can give us nontrivial insights about the barrier problems in circuit complexity, and that they need not…

The composite rotation approach has been used to develop a range of robust quantum logic gates, including single qubit gates and two qubit gates, which are resistant to systematic errors in their implementation. Single qubit gates based on…

Separation logic adds two connectives to assertion languages: separating conjunction * ("star") and its adjoint, separating implication -* ("magic wand"). Comparatively, separating implication is less widely used. This paper demonstrates…

Exploiting the effects of quantum interference we put forward an idea of designing three primary logic gates, OR, AND and NOT, using a benzene molecule. Under a specific molecule-lead interface geometry, anti-resonant states appear which…

Reversible logic circuits have been historically motivated by theoretical research in low-power electronics as well as practical improvement of bit-manipulation transforms in cryptography and computer graphics. Recently, reversible circuits…

Chip designers outsource chip fabrication to external foundries, but at the risk of IP theft. Logic locking, a promising solution to mitigate this threat, adds extra logic gates (key gates) and inputs (key bits) to the chip so that it…

Logic Encryption is one of the most popular hardware security techniques which can prevent IP piracy and illegal IC overproduction. It introduces obfuscation by inserting some extra hardware into a design to hide its functionality from…

The three-spin-$1/2$ decoherence-free subsystem defines a logical qubit protected from collective noise and supports exchange-only universal gates. Such logical qubits are well-suited for implementation with electrically-defined quantum…

As large language models (LLMs) are increasing integrated into fact-checking pipelines, formal logic is often proposed as a rigorous means by which to mitigate bias, errors and hallucinations in these models' outputs. For example, some…

Quantum annealers (QA), such as D-Wave systems, become increasingly efficient and competitive at solving combinatorial optimization problems. However, solving problems that do not directly map the chip topology remains challenging for this…

Transversal logical gates offer the opportunity for fast and low-noise logic, particularly when interspersed by a single round of parity check measurements of the underlying code. Using such circuits for the surface code requires decoding…

Conventional logic and memory devices are built out of deterministic units such as transistors, or magnets with energy barriers in excess of 40-60 kT. We show that stochastic units, p-bits, can be interconnected to create robust…

Singlet fission, a process that splits a singlet exciton into a biexciton, has promise in quantum information. We report time-resolved electron paramagnetic resonance measurements on a molecule, TIPS-BP1$'$, designed to exhibit strongly…

Thirty years ago, I introduced a non-commutative variant of classical linear logic, called "pomset logic", issued from a particular categorical interpretation of linear logic known as coherence spaces. In addition to the usual commutative…

We show that it is coNP-complete to decide whether a given proof structure of pomset logic is a correct proof net, using the graph-theoretic used in a previous paper of ours (arXiv:1901.10247).

The correctness of many algorithms and data structures depends on reachability properties, that is, on the existence of chains of references between objects in the heap. Reasoning about reachability is difficult for two main reasons. First,…

There is a recent trend in artificial intelligence (AI) inference towards lower precision data formats down to 8 bits and less. As multiplication is the most complex operation in typical inference tasks, there is a large demand for…

The Chua's circuit is examined using a State Controlled-Cellular Neural Network (SC-CNN) framework with two logical square wave input signals. We illustrate, in particular, that this nonlinear circuit can generate all the basic logic…