Related papers: Representations of Circular Words
We show how to derive new instances of the cyclic sieving phenomenon from old ones via elementary representation theory. Examples are given involving objects such as words, parking functions, finite fields, and graphs.
I propose a class of non-positional numeral systems where numbers are represented by Dyck words, with the systems arising from a recursive extension of prime factorization. After describing two proper subsets of the Dyck language capable of…
This paper provides a geometric characterization of subclasses of the regular languages. We use finite model theory to characterize objects like strings and trees as relational structures. Logical statements meeting certain criteria over…
Word embedding maps words into a low-dimensional continuous embedding space by exploiting the local word collocation patterns in a small context window. On the other hand, topic modeling maps documents onto a low-dimensional topic space, by…
We introduce a model for constructing vector representations of words by composing characters using bidirectional LSTMs. Relative to traditional word representation models that have independent vectors for each word type, our model requires…
A word-representable graph is a simple graph $G$ which can be represented by a word $w$ over the vertices of $G$ such that any two vertices are adjacent in $G$ if and only if they alternate in $w$. It is known that the class of…
Distributed representations of words have been shown to capture lexical semantics, as demonstrated by their effectiveness in word similarity and analogical relation tasks. But, these tasks only evaluate lexical semantics indirectly. In this…
The left-corner transform removes left-recursion from (probabilistic) context-free grammars and unification grammars, permitting simple top-down parsing techniques to be used. Unfortunately the grammars produced by the standard left-corner…
The clone of term operations of an algebraic structure consists of all operations that can be expressed by a term in the language of the structure. We consider bounds for the length and the height of the terms expressing these functions,…
A number theoretic algorithm is given for writing gauge theory amplitudes in a compact manner. It is possible to write down all details of the complete $L$ loop amplitude with two integers, or a complex integer. However, a more symmetric…
Morphisms are homomorphisms under the concatenation operation of the set of words over a finite set. Changing the elements of the finite set does not essentially change the morphism. We propose a way to select a unique representing member…
The literal and the initial literal shuffle have been introduced to model the behavior of two synchronized processes. However, it is not possible to describe the synchronization of multiple processes. Furthermore, both restricted forms of…
A circular program contains a data structure whose definition is self-referential or recursive. The use of such a definition allows efficient functional programs to be written and can avoid repeated evaluations and the creation of…
Knowledge representation and reasoning in law are essential to facilitate the automation of legal analysis and decision-making tasks. In this paper, we propose a new approach based on legal science, specifically legal taxonomy, for…
Inflection graphs are highly complex networks representing relationships between inflectional forms of words in human languages. For so-called synthetic languages, such as Latin or Polish, they have particularly interesting structure due to…
Word representation has always been an important research area in the history of natural language processing (NLP). Understanding such complex text data is imperative, given that it is rich in information and can be used widely across…
A graph $G=(V,E)$ is word-representable if there exists a word $w$ over the alphabet $V$ such that letters $x$ and $y$, $x\neq y$, alternate in $w$ if and only if $(x,y)\in E$. Halld\'{o}rsson et al.\ have shown that a graph is…
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…
A new mathematical notation is proposed for the iteration of functions. It facilitates the application of the iteration of functions in mathematical and logical expressions, definitions of sets, and formulations of algorithms. Illustrations…
This paper is the extended version of On the Complexity of Infinite Advice Strings (ICALP 2018). We investigate a notion of comparison between infinite strings. In a general way, if M is a computation model (e.g. Turing machines) and C a…