Related papers: M-Ambiguity Sequences for Parikh Matrices and Thei…

The word inference problem is to determine languages such that the information on the number of occurrences of those subwords in the language can uniquely identify a word. A considerable amount of work has been done on this problem, but the…

Parikh matrices have been a powerful tool in arithmetizing words by numerical quantities. However, the dependence on the ordering of the alphabet is inherited by Parikh matrices. Strong M-equivalence is proposed as a canonical alternative…

We have introduced a q-deformation, i.e., a polynomial in q with natural coefficients, of the binomial coefficient of two finite words u and v counting the number of occurrences of v as a subword of u. In this paper, we examine the…

We introduce the notion of general prints of a word, which is substantialized by certain canonical decompositions, to study repetition in words. These associated decompositions, when applied recursively on a word, result in what we term as…

Parikh matrices have been extensively investigated due to their usefulness in studying subword occurrences in words. Due to the dependency of Parikh matrices on the ordering of the alphabet, strong M-equivalence was proposed as an…

Certain upper triangular matrices, termed as Parikh matrices, are often used in the combinatorial study of words. Given a word, the Parikh matrix of that word elegantly computes the number of occurrences of certain predefined subwords in…

The commutative ambiguity of a context-free grammar G assigns to each Parikh vector v the number of distinct leftmost derivations yielding a word with Parikh vector v. Based on the results on the generalization of Newton's method to…

We introduce and study a generalized Parikh matrix mapping based on tracking the occurrence counts of special types of subsequences. These matrices retain more information about a word than the original Parikh matrix mapping while…

The focus of this work is the study of Parikh matrices with emphasis on two concrete problems. In the first part of our presentation we show that a conjecture by Dick at al. in 2021 only stands in the case of ternary alphabets, while…

Ambiguity is a natural language phenomenon occurring at different levels of syntax, semantics, and pragmatics. It is widely studied; in Psycholinguistics, for instance, we have a variety of competing studies for the human disambiguation…

Spurious ambiguity is the phenomenon whereby distinct derivations in grammar may assign the same structural reading, resulting in redundancy in the parse search space and inefficiency in parsing. Understanding the problem depends on…

We generalize the familiar notion of periodicity in sequences to a new kind of pseudoperiodicity, and we prove some basic results about it. We revisit the results of a 2012 paper of Shevelev and reprove his results in a simpler and more…

The notion of almost periodicity nontrivially generalizes the notion of periodicity. Strongly almost periodic sequences (=uniformly recurrent infinite words) first appeared in the field of symbolic dynamics, but then turned out to be…

The class of Parikh word representable graphs were recently introduced. In this work, we further develop its general theory beyond the binary alphabet. Our main result shows that this class is equivalent to the class of bipartite…

The Parikh vector p(s) of a string s is defined as the vector of multiplicities of the characters. Parikh vector q occurs in s if s has a substring t with p(t)=q. We present two novel algorithms for searching for a query q in a text s. One…

Ambiguity is inherently present in many machine learning tasks, but especially for sequential models seldom accounted for, as most only output a single prediction. In this work we propose an extension of the Multiple Hypothesis Prediction…

Temporary syntactic ambiguities arise when the beginning of a sentence is compatible with multiple syntactic analyses. We inspect to which extent neural language models (LMs) exhibit uncertainty over such analyses when processing…

We consider the complexities of substitutive sequences over a binary alphabet. By studying various types of special words, we show that, knowing some initial values, its complexity can be completely formulated via a recurrence formula…

The extension of pattern avoidance from ordinary permutations to those on multisets gave birth to several interesting enumerative results. We study permutations on regular multisets, i.e., multisets in which each element occurs the same…

Fici and Saarela ([2]) conjectured that a binary word of length n contains at least $\lfloor n/4 \rfloor$ abelian squares. We slightly extend this conjecture and show that it holds in some special cases. In all other cases we have the…