Related papers: FO2(<,+1,~) on data trees, data tree automata and …
Inference of phylogenetic networks is of increasing interest in the genomic era. However, the extent to which phylogenetic networks are identifiable from various types of data remains poorly understood, despite its crucial role in…
We develop a purely set-theoretic formalism for binary trees and binary graphs. We define a category of binary automata, and display it as a fibred category over the category of binary graphs. We also relate the notion of binary graphs to…
You might know that the name "tree transducers" refers to various kinds of automata that compute functions on ranked trees, i.e. terms over a first-order signature. But have you ever wondered about how to remember what a macro tree…
FOLD-R++ is a new inductive learning algorithm for binary classification tasks. It generates an (explainable) normal logic program for mixed type (numerical and categorical) data. We present a customized FOLD-R++ algorithm with the ranking…
CCS can be considered as a most natural extension of finite state automata in which interaction is made possible thanks to parallel composition. We propose here a similar extension for top-down tree automata. We introduce a parallel…
We propose a general data structure CORoBTS for storing B-tree-like search trees dynamically in a cache-oblivious way combining the van Emde Boas memory layout with packed memory array. In the use of the vEB layout mostly search complexity…
We develop a general framework for the specification and implementation of systems whose executions are words, or partial orders, over an infinite alphabet. As a model of an implementation, we introduce class register automata, a one-way…
A foundational question in the theory of linear compartmental models is how to assess whether a model is structurally identifiable -- that is, whether parameter values can be inferred from noiseless data -- directly from the combinatorics…
We study the two-variable fragments D^2 and IF^2 of dependence logic and independence-friendly logic. We consider the satisfiability and finite satisfiability problems of these logics and show that for D^2, both problems are…
Information, stored or transmitted in digital form, is often structured. Individual data records are usually represented as hierarchies of their elements. Together, records form larger structures. Information processing applications have to…
Model trees provide an appealing way to perform interpretable machine learning for both classification and regression problems. In contrast to ``classic'' decision trees with constant values in their leaves, model trees can use linear…
An order-theoretic forest is a countable partial order such that the set of elements larger than any element is linearly ordered. It is an order-theoretic tree if any two elements have an upper-bound. The order type of a branch can be any…
We consider recognizable trace rewriting systems with level-regular contexts (RTL). A trace language is level-regular if the set of Foata normal forms of its elements is regular. We prove that the rewriting graph of a RTL is word-automatic.…
We consider first-order logic with monoidal quantifiers over words. We show that all languages with a neutral letter, definable using the addition numerical predicate are also definable with the order predicate as the only numerical…
Bayesian networks (BNs) are graphical \emph{first-order} probabilistic models that allow for a compact representation of large probability distributions, and for efficient inference, both exact and approximate. We introduce a…
Machine learned models often must abide by certain requirements (e.g., fairness or legal). This has spurred interested in developing approaches that can provably verify whether a model satisfies certain properties. This paper introduces a…
Decision trees are popular machine learning models that are simple to build and easy to interpret. Even though algorithms to learn decision trees date back to almost 50 years, key properties affecting their generalization error are still…
We study how to evaluate MSO queries with free variables on trees, within the framework of enumeration algorithms. Previous work has shown how to enumerate answers with linear-time preprocessing and delay linear in the size of each output,…
A type-2 computable real function is necessarily continuous; and this remains true for relative, i.e. oracle-based computations. Conversely, by the Weierstrass Approximation Theorem, every continuous f:[0,1]->R is computable relative to…
This paper presents a complete axiomatization of Monadic Second-Order Logic (MSO) over infinite trees. MSO on infinite trees is a rich system, and its decidability ("Rabin's Tree Theorem") is one of the most powerful known results…