Related papers: Folding Custom Gates with Verifier Input
The algebraic zigzag construction has recently been introduced as a combinatorial foundation for a higher dimensional notion of string diagram. For use in a proof assistant, a layout algorithm is required to determine the optimal rendering…
We introduce algorithms to visualize feature spaces used by object detectors. Our method works by inverting a visual feature back to multiple natural images. We found that these visualizations allow us to analyze object detection systems in…
Threshold secret sharing schemes do not prevent any malicious behavior of the dealer or shareholders and so we need verifiable secret sharing, to detect and identify the cheaters, to achieve fair reconstruction of a secret. The problem of…
This article is concerned with an example of complex planar geometry arising from flat origami challenges. The complexity of solution algorithms is illustrated, depending on the depth of the initial analysis of the problem, starting from…
First-order model counting (FOMC) is a computational problem that asks to count the models of a sentence in finite-domain first-order logic. In this paper, we argue that the capabilities of FOMC algorithms to date are limited by their…
We analyze the problem of folding one polyhedron, viewed as a metric graph of its edges, into the shape of another, similar to 1D origami. We find such foldings between all pairs of Platonic solids and prove corresponding lower bounds,…
Automatic verification deals with the validation by means of computers of correctness certificates. The related tools, usually called proof assistants or interactive provers, provide an interactive environment for the creation of formal…
Multiplier circuits play an important role in reversible computation, which is helpful in diverse areas such as low power CMOS design, optical computing, DNA computing and bioinformatics. Here we propose a new reversible multiplier circuit…
A foundational result in origami mathematics is Kawasaki and Justin's simple, efficient characterization of flat foldability for unassigned single-vertex crease patterns (where each crease can fold mountain or valley) on flat material. This…
Grover's algorithm relies on the superposition and interference of quantum mechanics, which is more efficient than classical computing in specific tasks such as searching an unsorted database. Due to the high complexity of quantum…
Verification is one of the central tasks in circuit and system design. While simulation and emulation are widely used, complete correctness can only be ensured based on formal proof techniques. But these approaches often have very high run…
We study the human-in-the-loop customs inspection scenario, where an AI-assisted algorithm supports customs officers by recommending a set of imported goods to be inspected. If the inspected items are fraudulent, the officers can levy extra…
K-fold cross-validation is a widely used tool for assessing classifier performance. The reproducibility crisis faced by artificial intelligence partly results from the irreproducibility of reported k-fold cross-validation-based performance…
In this paper we examine the potential of computer-assisted proof methods to be applied much more broadly than commonly recognized. More specifically, we contend that there are vast opportunities to derive useful mathematical results and…
Randomized smoothing is a recent and celebrated solution to certify the robustness of any classifier. While it indeed provides a theoretical robustness against adversarial attacks, the dimensionality of current classifiers necessarily…
We develop a new symbolic-numeric algorithm for the certification of singular isolated points, using their associated local ring structure and certified numerical computations. An improvement of an existing method to compute inverse systems…
Integer division instruction is generally expensive in most architectures. If the divisor is constant, the division can be transformed into combinations of several inexpensive integer instructions. This article discusses the classic…
Windowed recurrences are sliding window calculations where a function is applied iteratively across the window of data, and are ubiquitous throughout the natural, social, and computational sciences. In this monograph we explore the…
We introduce a private quantum money scheme with the note verification procedure based on Sampling Matching, a problem in the one-way communication complexity model introduced by Kumar et al.[Nature Communications 10, Article number: 4152].…
The use of origami in engineering has significantly expanded in recent years, spanning deployable structures across scales, folding robotics, and mechanical metamaterials. However, finding foldable paths can be a formidable task as the…