Related papers: Asymptotic Approximation by Regular Languages
We say that a language $L$ is \emph{constantly growing} if there is a constant $c$ such that for every word $u\in L$ there is a word $v\in L$ with $\vert u\vert<\vert v\vert\leq c+\vert u\vert$. We say that a language $L$ is…
The article continues the study of the genus of regular languages that the authors introduced in a 2012 paper. Generalizing a previous result, we produce a new family of regular languages on a two-letter alphabet having arbitrary high…
Understanding the neural basis of language comprehension in the brain has been a long-standing goal of various scientific research programs. Recent advances in language modelling and in neuroimaging methodology promise potential…
By virtue of linguistic compositionality, few syntactic rules and a finite lexicon can generate an unbounded number of sentences. That is, language, though seemingly high-dimensional, can be explained using relatively few degrees of…
Synthetic datasets constructed from formal languages allow fine-grained examination of the learning and generalization capabilities of machine learning systems for sequence classification. This article presents a new benchmark for machine…
Natural language allows us to refer to novel composite concepts by combining expressions denoting their parts according to systematic rules, a property known as \emph{compositionality}. In this paper, we study whether the language emerging…
Since the early Sixties and Seventies it has been known that the regular and context-free languages are characterized by definability in the monadic second-order theory of certain structures. More recently, these descriptive…
In this thesis, we study the place of regular languages within the communication complexity setting. In particular, we are interested in the non-deterministic communication complexity of regular languages. We show that a regular language…
Formal languages are sets of strings of symbols described by a set of rules specific to them. In this note, we discuss a certain class of formal languages, called regular languages, and put forward some elementary results. The properties of…
In this chapter we discuss the problem of enumerating distinct regular expressions by size and the regular languages they represent. We discuss various notions of the size of a regular expression that appear in the literature and their…
We consider the problem of computing the measure of a regular language of infinite binary trees. While the general case remains unsolved, we show that the measure of a language defined by a first-order formula with no descendant relation or…
A language $L$ is said to be dense if every word in the universe is an infix of some word in $L$. This notion has been generalized from the infix operation to arbitrary word operations $\varrho$ in place of the infix operation…
One of the most interesting questions concerning hierarchical control of discrete-event systems with partial observations is a condition under which the language observability is preserved between the original and the abstracted plant.…
This essay proposes an interpretive analogy between large language models (LLMs) and quasicrystals, systems that exhibit global coherence without periodic repetition, generated through local constraints. While LLMs are typically evaluated…
We continue the research on the generative capacity of contextual grammars where contexts are adjoined around whole words (externally) or around subwords (internally) which belong to special regular selection languages. All languages…
Linguistic evaluations of how well LMs generalize to produce or understand language often implicitly take for granted that natural languages are generated by symbolic rules. According to this perspective, grammaticality is determined by…
The atoms of a regular language are non-empty intersections of complemented and uncomplemented quotients of the language. Tight upper bounds on the number of atoms of a language and on the quotient complexities of atoms are known. We…
The height of a piecewise-testable language $L$ is the maximum length of the words needed to define $L$ by excluding and requiring given subwords. The height of $L$ is an important descriptive complexity measure that has not yet been…
A zero-one language L is a regular language whose asymptotic probability converges to either zero or one. In this case, we say that L obeys the zero-one law. We prove that a regular language obeys the zero-one law if and only if its…
Arguably, omega-regular languages play an important role as a specification formalism in many approaches to systems monitoring via runtime verification. However, since their elements are infinite words, not every omega-regular language can…