Related papers: On the Count of Trees

Graph transformations definable in logic can be described using the notion of transductions. By understanding transductions as a basic embedding mechanism, which captures the possibility of encoding one graph in another graph by means of…

We prime-encode the natural numbers via recursive factorisation, iterated to the exponents, generating a corpus of planar rooted trees equivalently represented as Dyck words. This forms a deterministic text endowed with internal rules.…

Large language models have demonstrated remarkable capabilities across many tasks, yet face significant challenges when dealing with recursive reasoning problems, those requiring the resolution of nested hierarchical structures. While prior…

Generative models reliant on sequential autoregression have been at the forefront of language generation for an extensive period, particularly following the introduction of widely acclaimed transformers. Despite its excellent performance,…

Causal inference remains a fundamental challenge for large language models. Recent advances in internal reasoning with large language models have sparked interest in whether state-of-the-art reasoning models can robustly perform causal…

Decision trees have long been recognized as models of choice in sensitive applications where interpretability is of paramount importance. In this paper, we examine the computational ability of Boolean decision trees in deriving, minimizing,…

Logical fallacy uses invalid or faulty reasoning in the construction of a statement. Despite the prevalence and harmfulness of logical fallacies, detecting and classifying logical fallacies still remains a challenging task. We observe that…

A leaf path language is a Boolean combination of sets of the form $\mathsf{{}^mE}^k L$, with $k \ge 1$ and $L$ a regular word language, which consist of those forests where the node labels in at least $k$ leaf-to-root paths make up a word…

Reverse search is a convenient method for enumerating structured objects, that can be used both to address theoretical issues and to solve data mining problems. This method has already been successfully developed to handle unordered trees.…

We propose a novel architecture for Graph Neural Networks that is inspired by the idea behind Tree Kernels of measuring similarity between trees by taking into account their common substructures, named fragments. By imposing a series of…

Counters that hold natural numbers are ubiquitous in modeling and verifying software systems; for example, they model dynamic creation and use of resources in concurrent programs. Unfortunately, such discrete counters often lead to…

By extending the breadth first search algorithm to any d-type critical or subcritical irreducible branching forest, we show that such forests may be encoded through d independent, integer valued, d-dimensional random walks. An application…

We target the problem of provably computing the equivalence between two complex expression trees. To this end, we formalize the problem of equivalence between two such programs as finding a set of semantics-preserving rewrite rules from one…

We study the question of whether a given regular language of finite trees can be defined in first-order logic. We develop an algebraic approach to address this question and we use it to derive several necessary and sufficient conditions for…

Data trees serve as an abstraction of structured data, such as XML documents. A number of specification formalisms for languages of data trees have been developed, many of them adhering to the paradigm of register automata, which is based…

This paper shows that over infinite trees, satisfiability is decidable for weak monadic second-order logic extended by the unbounding quantifier U and quantification over infinite paths. The proof is by reduction to emptiness for a certain…

Graph polynomials encode fundamental combinatorial invariants of graphs. Their computation is investigated using tree and path decomposition frameworks, with formal definitions of treewidth, k-trees, and pathwidth establishing the…

We prove a new formula for the generating function of multitype Cayley trees counted according to their degree distribution. Using this formula we recover and extend several enumerative results about trees. In particular, we extend some…

Standard methods of using categorical variables as predictors either endow them with an ordinal structure or assume they have no structure at all. However, categorical variables often possess structure that is more complicated than a linear…

We generalise various theorems for finding indiscernible trees and arrays to positive logic: based on an existing modelling theorem for s-trees, we prove modelling theorems for str-trees, str$_0$-trees (the reduct of str-trees that forgets…