Related papers: Counting Subwords and Regular Languages
We solve the word problem of the identity $x(yz) = (xy)(yz)$ by investigating a certain group describing the geometry of that identity. We also construct a concrete realization of the free system of rank~1 relative to the above identity
We consider several novel aspects of unique factorization in formal languages. We reprove the familiar fact that the set uf(L) of words having unique factorization into elements of L is regular if L is regular, and from this deduce an…
A lens is a single program that specifies two data transformations at once: one transformation converts data from source format to target format and a second transformation inverts the process. Over the past decade, researchers have…
Language modelling is regularly analysed at word, subword or character units, but syllables are seldom used. Syllables provide shorter sequences than characters, they can be extracted with rules, and their segmentation typically requires…
The physics of randomness and regularities for languages (mother tongues) and their lifetimes and family trees and for the second languages are studied in terms of two opposite processes; random multiplicative noise [1], and fragmentation…
A necessary and sufficient condition for an element of an algebra (in the sense of Universal Algebra) to be in the dominion of a subalgebra is given, in terms of transferable sets. This criterion is then used to formulate a more wieldy…
We study the class of languages that have membership proofs which can be verified by real-time finite-state machines using only a constant number of random bits, regardless of the size of their inputs. Since any further restriction on the…
Recognizable languages of finite words are part of every computer science cursus, and they are routinely described as a cornerstone for applications and for theory. We would like to briefly explore why that is, and how this word-related…
This study presents a fascinating linguistic property related to the number of letters in words and their corresponding numerical values. By selecting any arbitrary word, counting its constituent letters, and subsequently spelling out the…
Let $X_n = \{1,2,\dots,n\}$ be a finite set $(n\geq 2)$ and $T_n$ the full transformation semigroup on $X_n$. For a positive integer $l\leq n-1$, we define $$T_n(l) = \{\alpha\in T_n \colon \forall x,y\in X_n,\, |x-y| = l \;\Rightarrow\;…
A regular realizability (RR) problem is testing nonemptiness of intersection of some fixed language (filter) with given regular language. We study here complexity of RR problems. It appears that for any language L there exists RR problem…
We study the problem of deciding whether a given language is directed. A language $L$ is \emph{directed} if every pair of words in $L$ have a common (scattered) superword in $L$. Deciding directedness is a fundamental problem in connection…
A two-parameter model of word length measured by the number of syllables comprising it is proposed. The first parameter is dependent on language type, the second one - on text genre and reflects the degree of completion of synergetic…
We give a simple new proof that regular languages defined by first-order sentences with no quantifier alteration can be defined by such sentences in which only regular atomic formulas appear. Earlier proofs of this fact relied on arguments…
Enumerating the number of times one word occurs in another is a much-studied combinatorial subject. By utilizing a method that we call ``lexicographic extreme referencing'', we provide a formula for computing occurrences of one binary word…
We find generating functions for the number of words avoiding certain patterns or sets of patterns on at most 2 distinct letters and determine which of them are equally avoided. We also find the exact number of words avoiding certain…
Syntax connects words to each other in very specific ways. Two words are syntactically connected if they depend directly on each other. Syntactic connections usually happen within a sentence. Gathering all those connection across several…
Words are sequences of letters over a finite alphabet. We study two intimately related topics for this object: quasi-randomness and limit theory. With respect to the first topic we investigate the notion of uniform distribution of letters…
A natural language (or ordinary language) is a language that is spoken, written, or signed by humans for general-purpose communication, as distinguished from formal languages (such as computer-programming languages or the "languages" used…
It is well known that the "store language" of every pushdown automaton -- the set of store configurations (state and stack contents) that can appear as an intermediate step in accepting computations -- is a regular language. Here many…