Related papers: Quotient complexity of ideal languages

We examine the complexity of basic regular operations on languages represented by Boolean and alternating finite automata. We get tight upper bounds m+n and m+n+1 for union, intersection, and difference, 2^m+n and 2^m+n+1 for concatenation,…

Commutative languages with the semilinear property (SLIP) can be naturally recognized by real-time NLOG-SPACE multi-counter machines. We show that unions and concatenations of such languages can be similarly recognized, relying on -- and…

Piecewise testable languages are a subclass of the regular languages. There are many equivalent ways of defining them; Simon's congruence $\sim_k$ is one of the most classical approaches. Two words are $\sim_k$-equivalent if they have the…

We construct a hierarchy of regular languages such that the current language in the hierarchy can be accepted by 1-way quantum finite automata with a probability smaller than the corresponding probability for the preceding language in the…

We investigate the state complexity of the permutation operation, or the commutative closure, on Alphabetical Pattern Constraints (APC). This class corresponds to level $3/2$ of the Straubing-Th{\'e}rien Hierarchy and includes the finite,…

Given a countable set X (usually taken to be the natural numbers or integers), an infinite permutation, \pi, of X is a linear ordering of X. This paper investigates the combinatorial complexity of infinite permutations on the natural…

In a previous paper, we described the set of words that appear in the coding of smooth (resp. analytic) curves at arbitrary small scale. The aim of this paper is to compute the complexity of those languages.

We investigate a famous decision problem in automata theory: separation. Given a class of language C, the separation problem for C takes as input two regular languages and asks whether there exists a third one which belongs to C, includes…

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…

The present paper presents and proves a proposition concerning the time complexity of finite languages. It is shown herein, that for any finite language (a language for which the set of words composing it is finite) there is a Turing…

Language models (LMs) estimate a probability distribution over strings in a natural language; these distributions are crucial for computing perplexity and surprisal in linguistics research. While we are usually concerned with measuring…

An ideal is a classical object of study in the field of algebraic number theory. In maximal quadratic orders of number fields, ideals usually represented by the $\mathbb Z$-basis. This form of representation is used in most of the…

This paper proposes a general quantum algorithm that can be applied to any classical computer program. Each computational step is written using reversible operators, but the operators remain classical in that the qubits take on values of…

The representation of numbers by product states in quantum mechanics can be extended to the representation of words and word sequences in languages by product states. This can be used to study quantum systems that generate text that has…

We prove that, for any natural number n $\ge$ 1, we can find a finite alphabet $\Sigma$ and a finitary language L over $\Sigma$ accepted by a one-counter automaton, such that the $\omega$-power L $\infty$ := {w 0 w 1. .. $\in$ $\Sigma$…

We show that classical and quantum Kolmogorov complexity of binary strings agree up to an additive constant. Both complexities are defined as the minimal length of any (classical resp. quantum) computer program that outputs the…

Group languages are regular languages recognized by finite groups, or equivalently by finite automata in which each letter induces a permutation on the set of states. We investigate the separation problem for this class of languages: given…

A longstanding debate in semiotics centers on the relationship between linguistic signs and their corresponding semantics: is there an arbitrary relationship between a word form and its meaning, or does some systematic phenomenon pervade?…

The set of finite words over a well-quasi-ordered set is itself well-quasi-ordered. This seminal result by Higman is a cornerstone of the theory of well-quasi-orderings and has found numerous applications in computer science. However, this…

We introduce a method for analyzing the complexity of natural language processing tasks, and for predicting the difficulty new NLP tasks. Our complexity measures are derived from the Kolmogorov complexity of a class of automata --- {\it…