Related papers: Complexity of Proper Suffix-Convex Regular Languag…
This work is concerned with regular languages defined over large alphabets, either infinite or just too large to be expressed enumeratively. We define a generic model where transitions are labeled by elements of a finite partition of the…
We consider ideals and Boolean combinations of ideals. For the regular languages within these classes we give expressively complete automaton models. In addition, we consider general properties of regular ideals and their Boolean…
We define a new class of languages of $\omega$-words, strictly extending $\omega$-regular languages. One way to present this new class is by a type of regular expressions. The new expressions are an extension of $\omega$-regular expressions…
Motivated by work on bio-operations on DNA strings, we consider an outfix-guided insertion operation that can be viewed as a generalization of the overlap assembly operation on strings studied previously. As the main result we construct a…
Each language has its own complex systems of word, phrase, and sentence construction, the guiding principles of which are often summarized in grammar descriptions for the consumption of linguists or language learners. However, manual…
Human language can be described as a complex network of linked words. In such a treatment, each distinct word in language is a vertex of this web, and neighboring words in sentences are connected by edges. It was recently found (Ferrer and…
Techniques are developed for creating new and general language families of only semilinear languages, and for showing families only contain semilinear languages. It is shown that for language families L that are semilinear full trios, the…
Given a regular language L, we effectively construct a unary semigroup that recognizes the topological closure of L in the free unary semigroup relative to the variety of unary semigroups generated by the pseudovariety R of all finite…
We identify a subclass of the regular commutative languages that is closed under the iterated shuffle, or shuffle closure. In particular, it is regularity-preserving on this subclass. This subclass contains the commutative group languages…
In 2009, Shur published the following conjecture: Let $L$ be a power-free language and let $e(L)\subseteq L$ be the set of words of $L$ that can be extended to a bi-infinite word respecting the given power-freeness. If $u, v \in e(L)$ then…
We study cube-free words over arbitrary non-unary finite alphabets and prove the following structural property: for every pair $(u,v)$ of $d$-ary cube-free words, if $u$ can be infinitely extended to the right and $v$ can be infinitely…
Smooth words over an alphabet of non-negative integers $\{a,b\}$ are infinite words that are infinitely derivable, the most famous example being the Oldenburger-Kolakoski word over $\{1,2\}$. The main way to study their language is to…
Traditionally, formal languages are defined as sets of words. More recently, the alternative coalgebraic or coinductive representation as infinite tries, i.e., prefix trees branching over the alphabet, has been used to obtain compact and…
A word $w$ over an alphabet $\Sigma$ is a Lyndon word if there exists an order defined on $\Sigma$ for which $w$ is lexicographically smaller than all of its conjugates (other than itself). We introduce and study \emph{universal Lyndon…
Grammar refers to the system of rules that governs the structural organization and the semantic relations among linguistic units such as sentences, phrases, and words within a given language. In natural language processing, there remains a…
A subsequence of a word $w$ is a word $u$ such that $u = w[i_1] w[i_2] \cdots w[i_k]$, for some set of indices $1 \leq i_1 < i_2 < \dots < i_k \leq \vert w \vert$. A word $w$ is \emph{$k$-subsequence universal} over an alphabet $\Sigma$ if…
This paper describes Convex, a convex optimization modeling framework in Julia. Convex translates problems from a user-friendly functional language into an abstract syntax tree describing the problem. This concise representation of the…
A vector addition system (VAS) with an initial and a final marking and transition labels induces a language. In part because the reachability problem in VAS remains far from being well-understood, it is difficult to devise decision…
We introduce deterministic suffix-reading automata (DSA), a new automaton model over finite words. Transitions in a DSA are labeled with words. From a state, a DSA triggers an outgoing transition on seeing a word ending with the…
Globalization and multiculturalism continue to produce increasingly diverse speech varieties. Yet current spoken dialogue systems frequently fail on under-represented dialects and accents, often misidentifying the input language and causing…