Related papers: Computing the longest common prefix of a context-f…
A simple linear-time algorithm for constructing a linear context-free tree grammar of size O(rg + r g log (n/r g))for a given input tree T of size n is presented, where g is the size of a minimal linear context-free tree grammar for T, and…
The rational index of a context-free language $L$ is a function $f(n)$, such that for each regular language $R$ recognized by an automaton with $n$ states, the intersection of $L$ and $R$ is either empty or contains a word shorter than…
Cross-bifix-free sets are sets of words such that no prefix of any word is a suffix of any other word. In this paper, we introduce a general constructive method for the sets of cross-bifix-free binary words of fixed length. It enables us to…
Given a formal language L specified in various ways, we consider the problem of determining if L is nonempty. If L is indeed nonempty, we find upper and lower bounds on the length of the shortest string in L.
A border of a string is a non-empty prefix of the string that is also a suffix of the string, and a string is unbordered if it has no border other than itself. Loptev, Kucherov, and Starikovskaya [CPM 2015] conjectured the following: If we…
We consider the problem of constructing prefix-free codes in which a designated symbol, a space, can only appear at the end of codewords. We provide a linear-time algorithm to construct almost-optimal codes with this property, meaning that…
Prefix normal words are binary words that have no factor with more $1$s than the prefix of the same length. Finite prefix normal words were introduced in [Fici and Lipt\'ak, DLT 2011]. In this paper, we study infinite prefix normal words…
When augmented with the longest common prefix (LCP) array and some other structures, the suffix array can solve many string processing problems in optimal time and space. A compressed representation of the LCP array is also one of the main…
The longest common prefix array is a very advantageous data structure that, combined with the suffix array and the Burrows-Wheeler transform, allows to efficiently compute some combinatorial properties of a string useful in several…
Cross-bifix-free sets are sets of words such that no prefix of any word is a sufix of any other word. In this paper, we introduce a general constructive method for the sets of cross-bifix-free q-ary words of fixed length. It enables us to…
The relationship between the length of a word and the maximum length of its unbordered factors is investigated in this paper. Consider a finite word w of length n. We call a word bordered, if it has a proper prefix which is also a suffix of…
When can two regular word languages K and L be separated by a simple language? We investigate this question and consider separation by piecewise- and suffix-testable languages and variants thereof. We give characterizations of when two…
This paper presents prefix codes which minimize various criteria constructed as a convex combination of maximum codeword length and average codeword length or maximum redundancy and average redundancy, including a convex combination of the…
A non-empty word $w$ is a \emph{border} of a word $u$ if $\vert w\vert<\vert u\vert$ and $w$ is both a prefix and a suffix of $u$. A word $u$ is \emph{privileged} if $\vert u\vert\leq 1$ or if $u$ has a privileged border $w$ that appears…
Language models for speech recognition typically use a probability model of the form Pr(a_n | a_1, a_2, ..., a_{n-1}). Stochastic grammars, on the other hand, are typically used to assign structure to utterances. A language model of the…
Probabilistic context-free grammars have a long-term record of use as generative models in machine learning and symbolic regression. When used for symbolic regression, they generate algebraic expressions. We define the latter as equivalence…
Let $\Sigma = X\cup X^{-1} = \{ x_1 ,x_2 ,..., x_m ,x_1^{-1} ,x_2^{-1} ,..., x_m^{-1} \}$ and let $G$ be a group with set of generators $\Sigma$. Let $\mathfrak{L} (G) =\left\{ \left. \omega \in \Sigma^* \; \right\vert \;\omega \equiv e \;…
The longest common extension problem (LCE problem) is to construct a data structure for an input string $T$ of length $n$ that supports LCE$(i,j)$ queries. Such a query returns the length of the longest common prefix of the suffixes…
A \emph{border} of a word $w$ is a word that is both a non-empty proper prefix and suffix of $w$. If $w$ has a border, then it is said to be \emph{bordered}; otherwise, it is said to be \emph{unbordered}. The main results of this paper are…
In this article, we provide three coalgebraic characterizations of the class of context-free languages, each based on the idea of adding coalgebraic structure to an existing algebraic structure by specifying output-derivative pairs. Final…