Related papers: Mapping words to powers by morphisms
Propositional logics in general, considered as a set of sentences, can be undecidable even if they have "nice" representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already…
Given a language L and a nondeterministic finite automaton M, we consider whether we can determine efficiently (in the size of M) if M accepts at least one word in L, or infinitely many words. Given that M accepts at least one word in L, we…
An infinite permutation $\alpha$ is a linear ordering of $\mathbb N$. We study properties of infinite permutations analogous to those of infinite words, and show some resemblances and some differences between permutations and words. In this…
We consider words as a network of interacting letters, and approximate the probability distribution of states taken on by this network. Despite the intuition that the rules of English spelling are highly combinatorial (and arbitrary), we…
An infinite word is an infinite Lyndon word if it is smaller, with respect to the lexicographic order, than all its proper suffixes, or equivalently if it has infinitely many finite Lyndon words as prefixes. A characterization of binary…
Rational word languages can be defined by several equivalent means: finite state automata, rational expressions, finite congruences, or monadic second-order (MSO) logic. The robust subclass of aperiodic languages is defined by: counter-free…
A morphism h is unambiguous with respect to a word w if there is no other morphism g that maps w to the same image as h. In the present paper we study the question of whether, for any given word, there exists an unambiguous 1-uniform…
Data-driven most powerful tests are statistical hypothesis decision-making tools that deliver the greatest power against a fixed null hypothesis among all corresponding data-based tests of a given size. When the underlying data…
Analogical proportions are statements expressed in the form "A is to B as C is to D" and are used for several reasoning and classification tasks in artificial intelligence and natural language processing (NLP). In this paper, we focus on…
We introduce a new methodology for intrinsic evaluation of word representations. Specifically, we identify four fundamental criteria based on the characteristics of natural language that pose difficulties to NLP systems; and develop tests…
We consider the satisfiability problem for the two-variable fragment of the first-order logic extended with modulo counting quantifiers and interpreted over finite words or trees. We prove a small-model property of this logic, which gives a…
We consider variations on the following problem: given an NFA M and a pattern p, does there exist an x in L(M) such that p matches x? We consider the restricted problem where M only accepts a finite language. We also consider the variation…
We introduce subsequence covers (s-covers, in short), a new type of covers of a word. A word $C$ is an s-cover of a word $S$ if the occurrences of $C$ in $S$ as subsequences cover all the positions in $S$. The s-covers seem to be…
Most state-of-the-art systems today produce morphological analysis based only on orthographic patterns. In contrast, we propose a model for unsupervised morphological analysis that integrates orthographic and semantic views of words. We…
In the setting of minimal local grammar-based coding, the input string is represented as a grammar with the minimal output length defined via simple symbol-by-symbol encoding. This paper discusses four contributions to this field. First, we…
Regular nested word languages (a.k.a. visibly pushdown languages) strictly extend regular word languages, while preserving their main closure and decidability properties. Previous works have shown that considering languages of 2-nested…
Zimin words are very special finite words which are closely related to the pattern-avoidability problem. This problem consists in testing if an instance of a given pattern with variables occurs in almost all words over any finite alphabet.…
Most popular word embedding techniques involve implicit or explicit factorization of a word co-occurrence based matrix into low rank factors. In this paper, we aim to generalize this trend by using numerical methods to factor higher-order…
We revisit the topic of power-free morphisms, focusing on the properties of the class of complementary morphisms. Such morphisms are defined over a $2$-letter alphabet, and map the letters 0 and 1 to complementary words. We prove that every…
If an infinite non-periodic word is uniformly recurrent or is of bounded repetition, then the limit of its periodicity complexity is infinity. Moreover, there are uniformly recurrent words with the periodicity complexity arbitrarily high at…