Related papers: Version Space Algebras are Acyclic Tree Automata

Decision trees and random forest remain highly competitive for classification on medium-sized, standard datasets due to their robustness, minimal preprocessing requirements, and interpretability. However, a single tree suffers from high…

The long-standing aspiration for software reuse has made astonishing strides in the past few years. Many modern software development ecosystems now come with rich sets of publicly-available components contributed by the community.…

As a common method in Machine Learning, Ensemble Method is used to train multiple models from a data set and obtain better results through certain combination strategies. Stacking method, as representatives of Ensemble Learning methods, is…

Compositionality is a key property for dealing with complexity, which has been studied from many points of view in diverse fields. Particularly, the composition of individual computations (or programs) has been widely studied almost since…

Ensemble methods such as random forests have transformed the landscape of supervised learning, offering highly accurate prediction through the aggregation of multiple weak learners. However, despite their effectiveness, these methods often…

Dense and sparse tensors allow the representation of most bulk data structures in computational science applications. We show that sparse tensor algebra can also be used to express many of the transformations on these datasets, especially…

Computer Algebra Systems (e.g. Maple) are used in research, education, and industrial settings. One of their key functionalities is symbolic integration, where there are many sub-algorithms to choose from that can affect the form of the…

Variable Elimination (VE) is a classical exact inference algorithm for probabilistic graphical models such as Bayesian Networks, computing the marginal distribution of a subset of the random variables in the model. Our goal is to understand…

In this paper we deal with three models of weighted automata that take weights in the field of real numbers. The first of these models are classical weighted finite automata, the second one are crisp-deterministic weighted automata, and the…

Algebraic characterization of logic programs has received increasing attention in recent years. Researchers attempt to exploit connections between linear algebraic computation and symbolic computation in order to perform logical inference…

We construct a quasi-coherent sheaf of associative algebras which controls a category of $AV$-modules over a smooth quasi-projective variety. We establish a local structure theorem, proving that in \'etale charts these associative algebras…

Field-guided parametrization methods have proven effective for quad meshing of surfaces; these methods compute smooth cross fields to guide the meshing process and then integrate the fields to construct a discrete mesh. A key challenge in…

We investigate compositional structures in data embeddings from pre-trained vision-language models (VLMs). Traditionally, compositionality has been associated with algebraic operations on embeddings of words from a pre-existing vocabulary.…

First-order logic is a natural way of expressing properties of computation. It is traditionally used in various program logics for expressing the correctness properties and certificates. Although such representations are expressive for some…

Program source code contains complex structure information, which can be represented in structured data forms like trees or graphs. To acquire the structural information in source code, most existing researches use abstract syntax trees…

The lexical and syntactic disparities among different programming languages (e.g., Java and Python) pose significant challenges for multi-language software engineering tasks such as cross-language code clone detection and code retrieval,…

The use of rewriting-based visual formalisms is on the rise. In the formal methods community, this is due also to the introduction of adhesive categories, where most properties of classical approaches to graph transformation, such as those…

A variant of Turing machines is introduced where the tape is replaced by a single tree which can be manipulated in a style akin to purely functional programming. This yields two benefits: first, the extra structure on the tape can be…

In order to gain a better understanding of the state space of programs, with the aim of making their verification more tractable, models based on directed topological spaces have been introduced, allowing to take in account equivalence…

We introduce Joint Probability Trees (JPT), a novel approach that makes learning of and reasoning about joint probability distributions tractable for practical applications. JPTs support both symbolic and subsymbolic variables in a single…