Related papers: Balancing lists: a proof pearl
Provably correct software is one of the key challenges in our softwaredriven society. While formal verification establishes the correctness of a given program, the result of program synthesis is a program which is correct by construction.…
This paper presents a program analysis method that generates program summaries involving polynomial arithmetic. Our approach builds on prior techniques that use solvable polynomial maps for summarizing loops. These techniques are able to…
Comparing alternatives in pairs is a very well known technique of ranking creation. The answer to how reliable and trustworthy ranking is depends on the inconsistency of the data from which it was created. There are many indices used for…
Guessing Random Additive Noise Decoding (GRAND) and its variants, known for their near-maximum likelihood performance, have been introduced in recent years. One such variant, Segmented GRAND, reduces decoding complexity by generating only…
In program semantics and verification, reasoning about loops is complicated by the need to produce two separate mathematical arguments: an invariant, for functional properties (ignoring termination); and a variant, for termination (ignoring…
Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…
We prove identifiability of the tree parameters of the 3-class Jukes-Cantor mixture model. The proof uses ideas from algebraic statistics, in particular: finding phylogenetic invariants that separate the varieties associated to different…
We propose methods to strengthen the invariance properties of representations obtained by contrastive learning. While existing approaches implicitly induce a degree of invariance as representations are learned, we look to more directly…
This study is about inducing classifiers using data that is imbalanced, with a minority class being under-represented in relation to the majority classes. The first section of this research focuses on the main characteristics of data that…
Number types for exact computation are usually based on directed acyclic graphs. A poor graph structure can impair the efficency of their evaluation. In such cases the performance of a number type can be drastically improved by…
Containment-based trees encompass various handy structures such as B+-trees, R-trees and M-trees. They are widely used to build data indexes, range-queryable overlays, publish/subscribe systems both in centralized and distributed contexts.…
A method for creating a forest of model trees to fit samples of a function defined on images is described in several steps: down-sampling the images, determining a tree's hyperplanes, applying convolutions to the hyperplanes to handle small…
We present families of combinatorial classes described as trees with nodes that can carry one of two types of "flowers": integer partitions or integer compositions. Two parameters on the flowers of trees will be considered: the number of…
A list decoding scheme for universal polar codes is presented. Our scheme applies to the universal polar codes first introduced by Sasoglu and Wang, and generalized to processes with memory by the authors. These codes are based on the…
We consider the avoidance of patterns in inversion sequences that relate sorting via sorting machines including data structures such as pop stacks and stacks. Such machines have been studied under a variety of additional constraints and…
Decision trees are widely used for non-linear modeling, as they capture interactions between predictors while producing inherently interpretable models. Despite their popularity, performing inference on the non-linear fit remains largely…
We consider the classical problem of invariant generation for programs with polynomial assignments and focus on synthesizing invariants that are a conjunction of strict polynomial inequalities. We present a sound and semi-complete method…
Class imbalance, which is also called long-tailed distribution, is a common problem in classification tasks based on machine learning. If it happens, the minority data will be overwhelmed by the majority, which presents quite a challenge…
Decision trees have been a very popular class of predictive models for decades due to their interpretability and good performance on categorical features. However, they are not always robust and tend to overfit the data. Additionally, if…
We consider the problem of stabilizing an unstable plant driven by bounded noise over a digital noisy communication link, a scenario at the heart of networked control. To stabilize such a plant, one needs real-time encoding and decoding…