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Attributed tree transducers (atts) have been equipped with regular look-around (i.e., a preprocessing via an attributed relabeling) in order to obtain a more robust class of translations. Here we give further evidence of this robustness: we…

We present a generic tree-interpolation algorithm in the SMT context with quantifiers. The algorithm takes a proof of unsatisfiability using resolution and quantifier instantiation and computes interpolants (which may contain quantifiers).…

We consider a partial light-cone limit of a correlation function of the stress-tensor multiplet and identify an integrable structure emerging at one loop order of perturbation theory. It corresponds to a noncompact open spin chain with one…

We study an abstract notion of tree structure which lies at the common core of various tree-like discrete structures commonly used in combinatorics: trees in graphs, order trees, nested subsets of a set, tree-decompositions of graphs and…

In order to develop systems capable of modeling artificial life, we need to identify, which systems can produce complex behavior. We present a novel classification method applicable to any class of deterministic discrete space and time…

An automaton is universal if it accepts every possible input. We study the notion of u-universality, which asserts that the automaton accepts every input starting with u. Universality and u-universality are both EXPTIME-hard for…

A practical measure for the complexity of sequences of symbols (``strings'') is introduced that is rooted in automata theory but avoids the problems of Kolmogorov-Chaitin complexity. This physical complexity can be estimated for ensembles…

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…

We study effective randomness-preserving transformations of path-incompressible trees. Some path-incompressible trees with infinitely many paths do not compute perfect path-random trees with computable oracle-use. Sparse perfect…

Tree ensembles (TEs) find a multitude of practical applications. They represent one of the most general and accurate classes of machine learning methods. While they are typically quite concise in representation, their operation remains…

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…

This short note aims at proving that the isolation problem is undecidable for probabilistic automata with only one probabilistic transition. This problem is known to be undecidable for general probabilistic automata, without restriction on…

A deterministic finite automaton in which every non-empty set of states occurs as the image of the whole state set under the action of a suitable input word is called completely reachable. We characterize such automata in terms of graphs…

Multilingual translation suffers from computational redundancy, especially when translating into multiple languages simultaneously. In addition, translation quality can suffer for low-resource languages. To address this, we introduce…

Many data management applications must deal with data which is uncertain, incomplete, or noisy. However, on existing uncertain data representations, we cannot tractably perform the important query evaluation tasks of determining query…

We consider the problem of minimising the number of states in a multiplicity tree automaton over the field of rational numbers. We give a minimisation algorithm that runs in polynomial time assuming unit-cost arithmetic. We also show that a…

We investigate the separability of arbitrary dimensional tripartite sys- tems. By introducing a new operator related to transformations on the subsystems a necessary condition for the separability of tripartite systems is presented.

We divide the class of infinite computable trees into three types. For the first and second types, $0'$ computes a nontrivial self-embedding while for the third type $0''$ computes a nontrivial self-embedding. These results are optimal and…

Let $T$ be a weighted tree. The weight of a subtree $T_1$ of $T$ is defined as the product of weights of vertices and edges of $T_1$. We obtain a linear-time algorithm to count the sum of weights of subtrees of $T$. As applications, we…

Pre-training Transformer from large-scale raw texts and fine-tuning on the desired task have achieved state-of-the-art results on diverse NLP tasks. However, it is unclear what the learned attention captures. The attention computed by…