Related papers: The complexity of tangent words
There is no single definition of complexity (Edmonds 1999; Gershenson 2008; Mitchell 2009; De Domenico, et al., 2019), as it acquires different meanings in different contexts. A general notion is the amount of information required to…
A language L is prefix-free if, whenever words u and v are in L and u is a prefix of v, then u=v. Suffix-, factor-, and subword-free languages are defined similarly, where "subword" means "subsequence". A language is bifix-free if it is…
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…
We study density of rational languages under shift invariant probability measures on spaces of two-sided infinite words, which generalizes the classical notion of density studied in formal languages and automata theory. The density for a…
In this paper we explore a new hierarchy of classes of languages and infinite words and its connection with complexity classes. Namely, we say that a language belongs to the class $L_k$ if it is a subset of the catenation of $k$ languages…
We study the problem of automatically computing the time complexity of concurrent object-oriented programs. To determine this complexity we use intermediate abstract descriptions that record relevant information for the time analysis (cost…
The traditional study of plane and space algebraic curves by looking at their tangent vectors, curvatures and torsions provides geometric, but unfortunately not sufficient information about individual curves in order to be able to…
This is a survey on the geometry of warped products, without, or essentially with only soft, calculation. Somewhere in the paper, the goal was to give a synthetic account since existing approaches are rather analytic. Somewhere else, we…
We study the state complexity of regular operations in the class of ideal languages. A language L over an alphabet Sigma is a right (left) ideal if it satisfies L = L Sigma* (L = Sigma* L). It is a two-sided ideal if L = Sigma* L Sigma *,…
A language $L$ over an alphabet $\Sigma$ is prefix-convex if, for any words $x,y,z\in\Sigma^*$, whenever $x$ and $xyz$ are in $L$, then so is $xy$. Prefix-convex languages include right-ideal, prefix-closed, and prefix-free languages. We…
We give a basic overview of computational complexity, query complexity, and communication complexity, with quantum information incorporated into each of these scenarios. The aim is to provide simple but clear definitions, and to highlight…
Although information content is invariant up to an additive constant, the range of possible additive constants applicable to programming languages is so large that in practice it plays a major role in the actual evaluation of K(s), the…
We define the algorithmic complexity of a quantum state relative to a given precision parameter, and give upper bounds for various examples of states. We also establish a connection between the entanglement of a quantum state and its…
Written language is complex. A written text can be considered an attempt to convey a meaningful message which ends up being constrained by language rules, context dependence and highly redundant in its use of resources. Despite all these…
Text simplification reduces the language complexity of professional content for accessibility purposes. End-to-end neural network models have been widely adopted to directly generate the simplified version of input text, usually functioning…
Text generation rarely considers the control of lexical complexity, which limits its more comprehensive practical application. We introduce a novel task of lexical complexity controlled sentence generation, which aims at keywords to…
Word meaning has different aspects, while the existing word representation "compresses" these aspects into a single vector, and it needs further analysis to recover the information in different dimensions. Inspired by quantum probability,…
Prompted models have demonstrated impressive few-shot learning abilities. Repeated interactions at test-time with a single model, or the composition of multiple models together, further expands capabilities. These compositions are…
Classically, the time complexity of a first-order method is estimated by its number of gradient computations. In this paper, we study a more refined complexity by taking into account the `lingering' of gradients: once a gradient is computed…
We compared entropy for texts written in natural languages (English, Spanish) and artificial languages (computer software) based on a simple expression for the entropy as a function of message length and specific word diversity. Code text…