Related papers: Weighted Prefix Normal Words: Mind the Gap
A square-free word $w$ over a fixed alphabet $\Sigma$ is extremal if every word obtained from $w$ by inserting a single letter from $\Sigma$ (at any position) contains a square. Grytczuk et al. recently introduced the concept of extremal…
In this paper we consider the computational complexity of the following problems: given a DFA or NFA representing a regular language L over a finite alphabet Sigma is the set of all prefixes (resp., suffixes, factors, subwords) of all words…
We study words that barely avoid repetitions, for several senses of "barely". A squarefree (respectively, overlap-free, cubefree) word is irreducible if removing any one of its interior letters creates a square (respectively, overlap,…
A regular language $L$ is said to be prime, if it is not the product of two non-trivial languages. Martens et al. settled the exact complexity of deciding primality for deterministic finite automata in 2010. For finite languages, Mateescu…
In this paper, we extend the notion of Lyndon word to transfinite words. We prove two main results. We first show that, given a transfinite word, there exists a unique factorization in Lyndon words that are densely non-increasing, a…
The notion of a normal bit sequence was introduced by Borel in 1909; it was the first definition of an individual random object. Normality is a weak notion of randomness requiring only that all $2^n$ factors (substrings) of arbitrary…
We characterize binary words that have exactly two unbordered conjugates and show that they can be expressed as a product of two palindromes.
A finite word $w$ with $\vert w\vert=n$ contains at most $n+1$ distinct palindromic factors. If the bound $n+1$ is attained, the word $w$ is called \emph{rich}. Let $\Factor(w)$ be the set of factors of the word $w$. It is known that there…
A special inverse monoid is one defined by a presentation where all the defining relations have the form $r = 1$. By a result of Ivanov Margolis and Meakin the word problem for such an inverse monoid can often be reduced to the word problem…
A property of prefix codes called strong monotonicity is introduced, and it is proven that for a given source, a prefix code is optimal if and only if it is complete and strongly monotone.
An integer array y = y[1..n] is said to be feasible if and only if y[1] = n and, for every i \in 2..n, i \le i+y[i] \le n+1. A string is said to be indeterminate if and only if at least one of its elements is a subset of cardinality greater…
It has been shown in the indexing literature that there is an essential difference between prefix/range searches on the one hand, and predecessor/rank searches on the other hand, in that the former provably allows faster query resolution.…
A word is square-free if it does not contain nonempty factors of the form $XX$. In 1906 Thue proved that there exist arbitrarily long square-free words over a $3$-letter alphabet. It was proved recently [7] that among these words there are…
In this article, we define general normal forms for any logic that has propositional part and whose non-propositional connectives distribute over the finite disjunctions. We do not require the non-propositional connectives to be closed on…
Unfoldings are a well known partial-order semantics of P/T Petri nets that can be applied to various model checking or verification problems. For high-level Petri nets, the so-called symbolic unfolding generalizes this notion. A complete…
In this paper we introduce and study new notions of uniform recurrence in multidimensional words. A $d$-dimensional word is called \emph{uniformly recurrent} if for all $(s_1,\ldots,s_d)\in\mathbb{N}^d$ there exists $n\in\mathbb{N}$ such…
Spoken word recognition involves at least two basic computations. First is matching acoustic input to phonological categories (e.g. /b/, /p/, /d/). Second is activating words consistent with those phonological categories. Here we test the…
In this paper we investigate the descriptional complexity of knot theoretic problems and show upper bounds for planarity problem of signed and unsigned knot diagrams represented by Gauss words. Since a topological equivalence of knots can…
A prefix grammar is a context-free grammar whose nonterminals generate prefix-free languages. A prefix grammar $G$ is an ordinal grammar if the language $L(G)$ is well-ordered with respect to the lexicographic ordering. It is known that…
The question of whether all words in two real positive definite letters have only positive eigenvalues is addressed and settled (negatively). This question was raised some time ago in connection with a long-standing problem in theoretical…