Related papers: Parsing for Semidirectional Lambek Grammar is NP-C…
We propose a new type of representation learning method that models words, phrases and sentences seamlessly. Our method does not depend on word segmentation and any human-annotated resources (e.g., word dictionaries), yet it is very…
Linear programming on the Stiefel manifold (LPS) is studied for the first time. It aims at minimizing a linear objective function over the set of all $p$-tuples of orthonormal vectors in ${\mathbb R}^n$ satisfying $k$ additional linear…
This paper presents our segmentation system developed for the MLP 2017 shared tasks on cross-lingual word segmentation and morpheme segmentation. We model both word and morpheme segmentation as character-level sequence labelling tasks. The…
\emph{Focused sequent calculi} are a refinement of sequent calculi, where additional side-conditions on the applicability of inference rules force the implementation of a proof search strategy. Focused cut-free proofs exhibit a special…
This paper studies the computational complexity of disambiguation under probabilistic tree-grammars and context-free grammars. It presents a proof that the following problems are NP-hard: computing the Most Probable Parse (MPP) from a…
We define the syntax and reduction relation of a recursively typed lambda calculus with a parallel case-function (a parallel conditional). The reduction is shown to be confluent. We interpret the recursive types as information systems in a…
We show that reachability, repeated reachability, nontermination and unboundedness are NP-complete for Lossy Channel Machines that are flat, i.e., with no nested cycles in the control graph. The upper complexity bound relies on a fine…
Parse trees are fundamental syntactic structures in both computational linguistics and compilers construction. We argue in this paper that, in both fields, there are good incentives for model-checking sets of parse trees for some word…
Current algorithms for context-free parsing inflict a trade-off between ease of understanding, ease of implementation, theoretical complexity, and practical performance. No algorithm achieves all of these properties simultaneously. Might et…
Graph model generation from natural language description is an important task with many applications in software engineering. With the rise of large language models (LLMs), there is a growing interest in using LLMs for graph model…
Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct randomized algorithm for solving large, weakly constrained SDP…
The mathematical representation of semantics is a key issue for Natural Language Processing (NLP). A lot of research has been devoted to finding ways of representing the semantics of individual words in vector spaces. Distributional…
It is shown that the problem of computing the Strahler number of a binary tree given as a term is complete for the circuit complexity class uniform $\mathsf{NC}^1$. For several variants, where the binary tree is given by a pointer structure…
Pregroup grammars were developed in 1999 and stayed Lambek's preferred algebraic model of grammar. The set-theoretic semantics of pregroups, however, faces an ambiguity problem. In his latest book, Lambek suggests that this problem might be…
It is known that different categorial grammars have surface representation in a fragment of first order multiplicative linear logic (MLL1). We show that the fragment of interest is equivalent to the recently introduced extended tensor type…
In 2018, it was shown that all finitely generated virtually Abelian groups have multiple context-free word problems, and it is still an open problem as to where to precisely place the word problems of hyperbolic groups in the formal…
Let $S$ be a semitopological semigroup and $\mathcal{CB}(S)$ denotes the $C^*$-algebra of all bounded complex valued continuous functions on $S$ with uniform norm. A function $f\in \mathcal{CB}(S)$ is left multiplicative \linebreak…
We study Semidefinite Programming, \SDPc relaxations for Sensor Network Localization, \SNLc with anchors and with noisy distance information. The main point of the paper is to view \SNL as a (nearest) Euclidean Distance Matrix, \EDM,…
Formulae of the Lambek calculus are constructed using three binary connectives, multiplication and two divisions. We extend it using a unary connective, positive Kleene iteration. For this new operation, following its natural…
Sparse dictionary learning (SDL) has become a popular method for adaptively identifying parsimonious representations of a dataset, a fundamental problem in machine learning and signal processing. While most work on SDL assumes a training…