Related papers: Unambiguous separators for tropical tree automata

Tropical geometry with the max-plus algebra has been applied to statistical learning models over tree spaces because geometry with the tropical metric over tree spaces has some nice properties such as convexity in terms of the tropical…

This paper presents the first step of a wider research effort to apply tree automata completion to the static analysis of functional programs. Tree Automata Completion is a family of techniques for computing or approximating the set of…

We give another proof of a theorem of Fife - understood broadly as providing a finite automaton that gives a complete description of all infinite binary overlap-free words. Our proof is significantly simpler than those in the literature. As…

This paper proposes a tropical geometry-based edge detection framework that reformulates convolution and gradient computations using min-plus and max-plus algebra. The tropical formulation emphasizes dominant intensity variations,…

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 multidimensional optimization problems, which are formulated and solved in terms of tropical mathematics. The problems are to minimize (maximize) a linear or nonlinear function defined on vectors over an idempotent semifield,…

Hyper-minimization is a state reduction technique that allows a finite change in the semantics. The theory for hyper-minimization of deterministic weighted tree automata is provided. The presence of weights slightly complicates the…

The \it{Ambient Logic} (AL) has been proposed for expressing properties of process mobility in the calculus of Mobile Ambients (MA), and as a basis for query languages on semistructured data. We study some basic questions concerning the…

We introduce an improved version of rational equivalence in tropical intersection theory which can be seen as a replacement of chapter 8 of our previous article arXiv:0709.3705v2. Using this new definition, rational equivalence is…

Due to the works of S. Bozapalidis and A. Alexandrakis, there is a well-known characterization of recognizable weighted tree languages over fields in terms of finite-dimensionality of syntactic vector spaces. Here we prove a…

Infinite words, also known as streams, hold significant interest in computer science and mathematics, raising the natural question of how their complexity should be measured. We introduce cellular automaton reducibility as a measure of…

Decision tree optimization is fundamental to interpretable machine learning. The most popular approach is to greedily search for the best feature at every decision point, which is fast but provably suboptimal. Recent approaches find the…

A process algebra is proposed, whose semantics maps a term to a nondeterministic finite automaton (NFA, for short). We prove a representability theorem: for each NFA $N$, there exists a process algebraic term $p$ such that its semantics is…

We study trees where each successor set is equipped with some additional structure. We introduce a family of automaton models for such trees and prove their equivalence to certain fixed-point logics. As a consequence we obtain…

We study the notion of sparseness for regular languages over finite trees and infinite words. A language of trees is called sparse if the relative number of $n$-node trees in the language tends to zero, and a language of infinite words is…

Model interpretability has become an important problem in machine learning (ML) due to the increased effect that algorithmic decisions have on humans. Counterfactual explanations can help users understand not only why ML models make certain…

A finite automaton is called bideterministic if it is both deterministic and codeterministic -- that is, if it is deterministic and its transpose is deterministic as well. The study of such automata in a weighted setting is initiated. All…

We present a new approach to the global fairness verification of tree-based classifiers. Given a tree-based classifier and a set of sensitive features potentially leading to discrimination, our analysis synthesizes sufficient conditions for…

We propose a new algebraic framework to discuss and classify recognizable tree languages, and to characterize interesting classes of such languages. Our algebraic tool, called preclones, encompasses the classical notion of syntactic…

Separation is a classical problem asking whether, given two sets belonging to some class, it is possible to separate them by a set from a smaller class. We discuss the separation problem for regular languages. We give a Ptime algorithm to…