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We consider injective first-order interpretations that input and output trees of bounded height. The corresponding functions have polynomial output size, since a first-order interpretation can use a k-tuple of input nodes to represent a…
Some Transformer-based models can perform cross-lingual transfer learning: those models can be trained on a specific task in one language and give relatively good results on the same task in another language, despite having been pre-trained…
We propose a bottom-up variant of Earley deduction. Bottom-up deduction is preferable to top-down deduction because it allows incremental processing (even for head-driven grammars), it is data-driven, no subsumption check is needed, and…
A transduction provides us with a way of using the monadic second-order language of a structure to make statements about a derived structure. Any transduction induces a relation on the set of these structures. This article presents a…
Transducers extend finite state automata with outputs, and describe transformations from strings to strings. Sequential transducers, which have a deterministic behaviour regarding their input, are of particular interest. However, unlike…
Sequence-to-sequence models have achieved impressive results on various tasks. However, they are unsuitable for tasks that require incremental predictions to be made as more data arrives or tasks that have long input sequences and output…
Two languages are separable by a piecewise testable language if and only if there exists no infinite tower between them. An infinite tower is an infinite sequence of strings alternating between the two languages such that every string is a…
All simple translation-invariant valuations on polytopes are classified. As a direct consequence the well-known conditions for translative-equidecomposability are recovered. Furthermore, a simplified proof of the classification of…
We show that deterministic collapsible pushdown automata of second order can recognize a language that is not recognizable by any deterministic higher-order pushdown automaton (without collapse) of any order. This implies that there exists…
We reveal an algorithm for determining the complete prefix code irreducibility (CPC-irreducibility) of dyadic trees labeled by a finite alphabet. By introducing an extended directed graph representation of tree shift of finite type (TSFT),…
We investigate the tree-to-tree functions computed by "affine $\lambda$-transducers": tree automata whose memory consists of an affine $\lambda$-term instead of a finite state. They can be seen as variations on Gallot, Lemay and Salvati's…
We show that equivalence of deterministic linear tree transducers can be decided in polynomial time when their outputs are interpreted over the free group. Due to the cancellation properties offered by the free group, the required…
Arc-standard derivations over projective dependency trees can be interpreted as the incremental construction of lexicalized ordered trees with contiguous yields. Each \textsc{shift}, \textsc{leftarc}, and \textsc{rightarc} transition…
Transformer model has been widely used on machine translation tasks and obtained state-of-the-art results. In this paper, we report an interesting phenomenon in its encoder-decoder multi-head attention: different attention heads of the…
We propose to study transformations on graphs, and more generally structures, by looking at how the cut-rank (as introduced by Oum) of subsets is affected when going from the input structure to the output structure. We consider…
Pushdown automata may contain transitions that are never used in any accepting run of the automaton. We present an algorithm for detecting such useless transitions. A finite automaton that captures the possible stack content during runs of…
In this functional pearl, we examine the use of definitional interpreters as a basis for abstract interpretation of higher-order programming languages. As it turns out, definitional interpreters, especially those written in monadic style,…
Weight-balanced trees are a popular form of self-balancing binary search trees. Their popularity is due to desirable guarantees, for example regarding the required work to balance annotated trees. While usual weight-balanced trees perform…
Interpretability is an important aspect of the trustworthiness of a model's predictions. Transformer's predictions are widely explained by the attention weights, i.e., a probability distribution generated at its self-attention unit (head).…
Top-down and bottom-up theorem proving approaches each have specific advantages and disadvantages. Bottom-up provers profit from strong redundancy control but suffer from the lack of goal-orientation, whereas top-down provers are…