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Recent advances in Neural Machine Translation (NMT) show that adding syntactic information to NMT systems can improve the quality of their translations. Most existing work utilizes some specific types of linguistically-inspired tree…
In this paper, we investigate the problem of synthesizing computable functions of infinite words over an infinite alphabet (data omega-words). The notion of computability is defined through Turing machines with infinite inputs which can…
Decision trees and their ensembles are popular in machine learning as easy-to-understand models. Several techniques have been proposed in the literature for learning tree-based classifiers, with different techniques working well for data…
Two results are presented concerning the entailment problem in Separation Logic with inductively defined predicate symbols and theory reasoning. First, we show that the entailment problem is undecidable for rules with bounded tree-width, if…
Deciding whether there is a single tree -a supertree- that summarizes the evolutionary information in a collection of unrooted trees is a fundamental problem in phylogenetics. We consider two versions of this question: agreement and…
It is well known that attributed tree transducers can be equipped with "regular look-around" in order to obtain a more robust class of translations. We present two characterizations of this class in terms of macro tree transducers (MTTs):…
This paper studies tree-automatic ordinals (or equivalently, well-founded linearly ordered sets) together with the ordinal addition operation +. Informally, these are ordinals such that their elements are coded by finite trees for which the…
Separation Logic is a widely used formalism for describing dynamically allocated linked data structures, such as lists, trees, etc. The decidability status of various fragments of the logic constitutes a long standing open problem. Current…
We prove decidability of the boundedness problem for monadic least fixed-point recursion based on positive monadic second-order (MSO) formulae over trees. Given an MSO-formula phi(X,x) that is positive in X, it is decidable whether the…
The definition of $k^{th}$-order empirical entropy of strings is extended to node labelled binary trees. A suitable binary encoding of tree straight-line programs (that have been used for grammar-based tree compression before) is shown to…
Understanding the evolution of a set of genes or species is a fundamental problem in evolutionary biology. The problem we study here takes as input a set of trees describing {possibly discordant} evolutionary scenarios for a given set of…
We consider the task of learning Ising models when the signs of different random variables are flipped independently with possibly unequal, unknown probabilities. In this paper, we focus on the problem of robust estimation of…
The HOM problem, which asks whether the image of a regular tree language under a given tree homomorphism is again regular, is known to be decidable [Godoy & Gim\'enez: The HOM problem is decidable. JACM 60(4), 2013]. However, the problem…
The transducer synthesis problem on finite words asks, given a specification $S \subseteq I \times O$, where $I$ and $O$ are sets of finite words, whether there exists an implementation $f: I \rightarrow O$ which (1) fulfils the…
A tie-breaking method is proposed for choosing the predicted class, or outcome, in a decision tree. The method is an adaptation of a similar technique used for deodata predictors.
We study finite-state transducers and their power for transforming infinite words. Infinite sequences of symbols are of paramount importance in a wide range of fields, from formal languages to pure mathematics and physics. While finite…
Mechanistic interpretability aims to break models into meaningful parts; verifying that two such parts implement the same computation is a prerequisite. Existing similarity measures evaluate either empirical behaviour, leaving them blind to…
Higher-order constrained Horn clauses (HoCHC) are a semantically-invariant system of higher-order logic modulo theories. With semi-decidable unsolvability over a semi-decidable background theory, HoCHC is suitable for safety verification.…
Daily internet communication relies heavily on tree-structured graphs, embodied by popular data formats such as XML and JSON. However, many recent generative (probabilistic) models utilize neural networks to learn a probability distribution…
This work concerns formal descriptions of DNA code properties, and builds on previous work on transducer descriptions of classic code properties and on trajectory descriptions of DNA code properties. This line of research allows us to give…