Related papers: Bottom-Up Derivatives of Tree Expressions

In structural proof theory, designing and working on large calculi make it difficult to get intuitions about each rule individually and as part of a whole system. We introduce two novel tools to help working on calculi using the approach of…

We consider the synthesis of deterministic tree transducers from automaton definable specifications, given as binary relations, over finite trees. We consider the case of specifications that are deterministic top-down tree automatic,…

We prove non-asymptotic stretched exponential tail bounds on the height of a randomly sampled node in a random combinatorial tree, which we use to prove bounds on the heights and widths of random trees from a variety of models. Our results…

Nominal set plays a central role in a group-theoretic extension of finite automata to those over an infinite set of data values. Moerman et al. proposed an active learning algorithm for nominal word automata with the equality symmetry. In…

It is well known that for a given bottom-up tree automaton it can be decided whether or not there exists deterministic top-down tree automaton that recognized the same tree language. Recently it was claimed that such a decision can be…

We prove complex contraction for zero-free regions of counting weighted set cover problem in which an element can appear in an unbounded number of sets, thus obtaining fully polynomial-time approximation schemes(FPTAS) via Barvinok's…

We exhibit the construction of a deterministic automaton that, given k > 0, recognizes the (regular) language of k-differentiable words. Our approach follows a scheme of Crochemore et al. based on minimal forbidden words. We extend this…

We propose a new arithmetic for non-empty rooted unordered trees simply called trees. After discussing tree representation and enumeration, we define the operations of tree addition, multiplication and stretch, prove their properties, and…

We show that an algorithmic construction of sequences of recursive trees leads to a direct proof of the convergence of random recursive trees in an associated Doob-Martin compactification; it also gives a representation of the limit in…

The hierarchical and recursive expressive capability of rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. On the other hand, such hierarchical…

This thesis is focused on techniques for finite automata and their use in practice, with the main emphasis on nondeterministic tree automata. This concerns namely techniques for size reduction and language inclusion testing, which are two…

In this paper, we define a new kind of weighted tree automata where the weights are only supported by final states. We show that these automata are sequentializable and we study their closures under classical regular and algebraic…

We present several results that rely on arguments involving the combinatorics of "bushy trees". These include the fact that there are arbitrarily slow-growing diagonally noncomputable (DNC) functions that compute no Kurtz random real, as…

Given an $\mathbb{N}$-weighted tree automaton, we give a decision procedure for exponential vs polynomial growth (with respect to the input size) in quadratic time, and an algorithm that computes the exact polynomial degree of growth in…

We introduce a new class of automata (which we coin EU-automata) running on infininte trees of arbitrary (finite) arity. We develop and study several algorithms to perform classical operations (union, intersection, complement, projection,…

This paper deals with graph automaton groups associated with trees and some generalizations. We start by showing some algebraic properties of tree automaton groups. Then we characterize the associated semigroup, proving that it is…

Bayesian Decision Trees are known for their probabilistic interpretability. However, their construction can sometimes be costly. In this article we present a general Bayesian Decision Tree algorithm applicable to both regression and…

We advance the recently proposed neuro-symbolic Differentiable Tree Machine, which learns tree operations using a combination of transformers and Tensor Product Representations. We investigate the architecture and propose two key…

In this work we introduce new generalised quantifiers which allow us to express the Rabin-Mostowski index of automata. Our main results study expressive power and decidability of the monadic second-order (MSO) logic extended with these…

A tree automatic structure is a structure whose domain can be encoded by a regular tree language such that each relation is recognisable by a finite automaton processing tuples of trees synchronously. Words can be regarded as specific…