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Many common sequential data sources, such as source code and natural language, have a natural tree-structured representation. These trees can be generated by fitting a sequence to a grammar, yielding a hierarchical ordering of the tokens in…
We use reinforcement learning to learn tree-structured neural networks for computing representations of natural language sentences. In contrast with prior work on tree-structured models in which the trees are either provided as input or…
In this paper, we provide algorithms to rank and unrank certain degree-restricted classes of Cayley trees (spanning trees of the n-vertex complete graph). Specifically, we consider classes of trees that have a given set of leaves or a fixed…
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…
Motivated by the properties of the descent polynomials, which enumerate permutations of $S_n$ with a fixed descent set, we define descent polynomials for labeled rooted trees. We give recursive and explicit formulas for these polynomials…
We re-examine a lower-tail upper bound for the random variable $$X=\prod_{i=1}^{\infty}\min\left\{\sum_{k=1}^iE_k,1\right\},$$ where $E_1,E_2,\ldots\stackrel{iid}\sim\text{Exp}(1)$. This bound has found use in root-finding and seed-finding…
Different from other sequential data, sentences in natural language are structured by linguistic grammars. Previous generative conversational models with chain-structured decoder ignore this structure in human language and might generate…
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…
This paper studies the complexity of languages of finite words using automata theory. To go beyond the class of regular languages, we consider infinite automata and the notion of state complexity defined by Karp. Motivated by the seminal…
Given a set $P$ of terminals in the plane and a partition of $P$ into $k$ subsets $P_1, ..., P_k$, a two-level rectilinear Steiner tree consists of a rectilinear Steiner tree $T_i$ connecting the terminals in each set $P_i$ ($i=1,...,k$)…
Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…
We suggest a compositional vector representation of parse trees that relies on a recursive combination of recurrent-neural network encoders. To demonstrate its effectiveness, we use the representation as the backbone of a greedy, bottom-up…
Tree ensemble models such as random forests and boosted trees are among the most widely used and practically successful predictive models in applied machine learning and business analytics. Although such models have been used to make…
Originally proposed for handling time series data, Auto-regressive Decision Trees (ARDTs) have not yet been explored for language modeling. This paper delves into both the theoretical and practical applications of ARDTs in this new context.…
We reduce phrase-representation parsing to dependency parsing. Our reduction is grounded on a new intermediate representation, "head-ordered dependency trees", shown to be isomorphic to constituent trees. By encoding order information in…
Weighted automata (WA) are an important formalism to describe quantitative properties. Obtaining equivalent deterministic machines is a longstanding research problem. In this paper we consider WA with a set semantics, meaning that the…
We address the non-redundant random generation of k words of length n from a context-free language. Additionally, we want to avoid a predefined set of words. We study the limits of a rejection-based approach, whose time complexity is shown…
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…
We study alternating automata with qualitative semantics over infinite binary trees: alternation means that two opposing players construct a decoration of the input tree called a run, and the qualitative semantics says that a run of the…
Motivated by the continuing interest in the tree data model, we study the expressive power of downward navigational query languages on trees and chains. Basic navigational queries are built from the identity relation and edge relations…