Related papers: Syntactic Complexity of Star-Free Languages
For a complexity function $C$, the lower and upper $C$-complexity rates of an infinite word $\mathbf{x}$ are \[ \underline{C}(\mathbf x)=\liminf_{n\to\infty} \frac{C(\mathbf{x}\upharpoonright n)}n,\quad \overline{C}(\mathbf…
The state complexity of the result of a regular operation is often positively correlated with the number of distinct transformations induced by letters in the minimal deterministic finite automaton of the input languages. That is, more…
The grammars of natural languages may be learned by using genetic algorithms that reproduce and mutate grammatical rules and part-of-speech tags, improving the quality of later generations of grammatical components. Syntactic rules are…
Motivated by the question of which completely regular semigroups have context-free word problem, we show that for certain classes of languages $\mathfrak{C}$(including context-free), every completely regular semigroup that is a union of…
The theory of finite automata concerns itself with words in a free monoid together with concatenation and without further structure. There are, however, important applications which use alphabets which are structured in some sense. We…
We fully classify automatic sequences $a$ over a finite alphabet $\Omega$ with the property that each word over $\Omega$ appears is $a$ along an arithmetic progression. Using the terminology introduced by Avgustinovich, Fon-Der-Flaass and…
In this paper we consider the state complexity of an operation on formal languages, root(L). This naturally entails the discussion of the monoid of transformations of a finite set. We obtain good upper and lower bounds on the state…
We study cellular automata with respect to a new communication complexity problem: each of two players know half of some finite word, and must be able to tell whether the state of the central cell will follow a given evolution, by…
A language L is suffix-convex if for any words u, v,w, whenever w and uvw are in L, vw is in L as well. Suffix-convex languages include left ideals, suffix-closed languages, and suffix-free languages, which were studied previously. In this…
We define a notion of randomness for individual and collections of formal languages based on automatic martingales acting on sequences of words from some underlying domain. An automatic martingale bets if the incoming word belongs to the…
We study regular expressions that use variables, or parameters, which are interpreted as alphabet letters. We consider two classes of languages denoted by such expressions: under the possibility semantics, a word belongs to the language if…
We introduce "synchronous algebras", an algebraic structure tailored to recognize automatic relations (aka. synchronous relations, or regular relations). They are the equivalent of monoids for regular languages, however they conceptually…
Regular synchronization languages can be used to define rational relations of finite words, and to characterize subclasses of rational relations, like automatic or recognizable relations. We provide a systematic study of the decidability of…
We study the state complexity of boolean operations and product (concatenation, catenation) combined with star. We derive tight upper bounds for the symmetric differences and differences of two languages, one or both of which are starred,…
Targeted syntactic evaluations of language models ask whether models show stable preferences for syntactically acceptable content over minimal-pair unacceptable inputs. Most targeted syntactic evaluation datasets ask models to make these…
The infimal prefix-closed, controllable and observable superlanguage plays an essential role in the relationship between controllability, observability and co-observability -- the central notions of supervisory control theory. Existing…
The Random Language Model (De Giuli 2019) is an ensemble of stochastic context-free grammars, quantifying the syntax of human and computer languages. The model suggests a simple picture of first language learning as a type of annealing in…
A right ideal is a language L over an alphabet A that satisfies L = LA*. We show that there exists a stream (sequence) (R_n : n \ge 3) of regular right ideal languages, where R_n has n left quotients and is most complex under the following…
We consider the state complexity of basic operations on tree languages recognized by deterministic unranked tree automata. For the operations of union and intersection the upper and lower bounds of both weakly and strongly deterministic…
The first step when forming the polynomial hierarchies of languages is to consider languages of the form KaL where K and L are over a finite alphabet A and from a given variety V of languages, a being a letter from A. All such KaL's…