Related papers: Solving non-linear Horn clauses using a linear sol…
Given two rooted, ordered, and labeled trees $P$ and $T$ the tree inclusion problem is to determine if $P$ can be obtained from $T$ by deleting nodes in $T$. This problem has recently been recognized as an important query primitive in XML…
Reconciliation methods aim at recovering macro evolutionary events and at localizing them in the species history, by observing discrepancies between gene family trees and species trees. In this article we introduce an Integer Linear…
Clustering serves as a vital tool for uncovering latent data structures, and achieving both high accuracy and interpretability is essential. To this end, existing methods typically construct binary decision trees by solving mixed-integer…
We call a CNF formula linear if any two clauses have at most one variable in common. We show that there exist unsatisfiable linear k-CNF formulas with at most 4k^2 4^k clauses, and on the other hand, any linear k-CNF formula with at most…
Prolog is a well known declarative programming language based on propositional Horn formulas. It is useful in various areas, including artificial intelligence, automated theorem proving, mathematical logic and so on. An active research area…
This paper explores the use of Column Generation (CG) techniques in constructing univariate binary decision trees for classification tasks. We propose a novel Integer Linear Programming (ILP) formulation, based on root-to-leaf paths in…
Learning linear combinations of multiple kernels is an appealing strategy when the right choice of features is unknown. Previous approaches to multiple kernel learning (MKL) promote sparse kernel combinations to support interpretability and…
We study restricted computation models related to the Tree Evaluation Problem}. The TEP was introduced in earlier work as a simple candidate for the (*very*) long term goal of separating L and LogDCFL. The input to the problem is a rooted,…
In this work, we consider adaptive linear programming (ALP) decoding of linear codes over the finite field $\mathbb{F}_p$ of size $p$ where $p$ is a prime. In particular, we provide a general construction of valid inequalities for the…
A sequential piecewise linear programming method is presented where bounded domains of non-convex functions are successively contracted about the solution of a piecewise linear program at each iteration of the algorithm. Although…
We present a method for automatic inference of conditions on the initial states of a program that guarantee that the safety assertions in the program are not violated. Constrained Horn clauses (CHCs) are used to model the program and…
Tree ensembles are very popular machine learning models, known for their effectiveness in supervised classification and regression tasks. Their performance derives from aggregating predictions of multiple decision trees, which are renowned…
Verification conditions (VCs) are logical formulas whose satisfiability guarantees program correctness. We consider VCs in the form of constrained Horn clauses (CHC) which are automatically generated from the encoding of (an interpreter of)…
This work addresses the problem of computing measures of recognisable sets of infinite trees. An algorithm is provided to compute the probability measure of a tree language recognisable by a weak alternating automaton, or equivalently…
Hermitian hulls of linear codes are interesting for theoretical and practical reasons alike. In terms of recent application, linear codes whose hulls meet certain conditions have been utilized as ingredients to construct…
Given two messages - as linear sequences of letters, it is immediate to determine whether one can be transformed into the other by simple substitution cipher of the letters. On the other hand, if the letters are carried as labels on nodes…
Neural networks with tree-based sentence encoders have shown better results on many downstream tasks. Most of existing tree-based encoders adopt syntactic parsing trees as the explicit structure prior. To study the effectiveness of…
We present HornStr, the first solver for invariant synthesis for Regular Model Checking (RMC) with the specification provided in the SMT-LIB 2.6 theory of strings. It is well-known that invariant synthesis for RMC subsumes various important…
This paper studies the "explanation problem" for tree- and linearly-ordered array data, a problem motivated by database applications and recently solved for the one-dimensional tree-ordered case. In this paper, one is given a matrix A whose…
We present a new method to solve nonlinear Hammerstein equations with weakly singular kernels. The process to approximate the solution, followed usually, consists in adapting the discretization scheme from the linear case in order to obtain…