Tootfinder

Derivation and Verification of Array Sorting by Merging, and its Certification in Dafny
Juan Pablo Carbonell, Jos\'e E. Solsona, Nora Szasz, \'Alvaro Tasistro
https://arxiv.org/abs/2509.01758

Derivation and Verification of Array Sorting by Merging, and its Certification in Dafny
We provide full certifications of two versions of merge sort of arrays in the verification-aware programming language Dafny. We start by considering schemas for applying the divide-and-conquer or partition method of solution to specifications given by pre- and post-conditions involving linear arrays. We then derive the merge sort and merging algorithms as instances of these schemas, thereby arriving at a fully recursive formulation. Further, the analysis of the tree of subproblems arising from …

Curve-based slicer for multi-axis DLP 3D printing
Chengkai Dai, Tao Liu, Dezhao Guo, Binzhi Sun, Guoxin Fang, Yeung Yam, Charlie C. L. Wang
https://arxiv.org/abs/2509.00040 http…

Curve-based slicer for multi-axis DLP 3D printing
This paper introduces a novel curve-based slicing method for generating planar layers with dynamically varying orientations in digital light processing (DLP) 3D printing. Our approach effectively addresses key challenges in DLP printing, such as regions with large overhangs and staircase artifacts, while preserving its intrinsic advantages of high resolution and fast printing speeds. We formulate the slicing problem as an optimization task, in which parametric curves are computed to define both…