Related papers: The complexity of tangent words
Dealing with the complex word forms in morphologically rich languages is an open problem in language processing, and is particularly important in translation. In contrast to most modern neural systems of translation, which discard the…
Classes of linguistic paradoxes and linguistic tautologies are introduced with examples and explanations. They are part of the author's work on the Paradoxist Philosophy based on mathematical logic. The general cases exposed below are…
The primary objects of study in the ``knot theory of complex plane curves'' are C-links: links (or knots) cut out of a 3-sphere in the complex plane by complex plane transverse and totally tangential. Transverse C-links are naturally…
We present a new method for inferring complexity properties for a class of programs in the form of flowcharts annotated with loop information. Specifically, our method can (soundly and completely) decide if computed values are polynomially…
We investigate the number of sets of words that can be formed from a finite alphabet, counted by the total length of the words in the set. An explicit expression for the counting sequence is derived from the generating function, and…
In this paper we introduce and study a new complexity measure for finite words. For positive integer $d$ special scattered subwords, called super-$d$-subwords, in which the gaps are of length at least $(d-1)$, are defined. We give methods…
In this paper we propose a calculus for expressing algorithms for programming languages transformations. We present the type system and operational semantics of the calculus, and we prove that it is type sound. We have implemented our…
In this work we study the space complexity of computable real numbers represented by fast convergent Cauchy sequences. We show the existence of families of trascendental numbers which are logspace computable, as opposed to algebraic…
We review possible measures of complexity which might in particular be applicable to situations where the complexity seems to arise spontaneously. We point out that not all of them correspond to the intuitive (or "naive") notion, and that…
Scientists have demonstrated that quantum computing has presented novel approaches to address computational challenges, each varying in complexity. Adapting problem-solving strategies is crucial to harness the full potential of quantum…
Does text have an intrinsic curvature? Language is increasingly modeled in curved geometries - hyperbolic spaces for hierarchy, mixed-curvature manifolds for compositional structure - yet a basic scientific question remains unresolved: what…
Various "hardness" measures have been studied for resolution, providing theoretical insight into the proof complexity of resolution and its fragments, as well as explanations for the hardness of instances in SAT solving. In this report we…
A systematic way of defining variants of a modeling language is useful for adopting the language to domain or project specific needs. Variants can be obtained by adopting the syntax or semantics of the language. In this paper, we take a…
Suppose that Alice and Bob are given each an infinite string, and they want to decide whether their two strings are in a given relation. How much communication do they need? How can communication be even defined and measured for infinite…
Recent studies showed that hardness, a complex property, can be calculated using very simple approaches or even analytical formulae. These form the basis for evaluating controversial experimental results (as we illustrate for…
We investigate the properties of formal languages expressible in terms of formulas over quantifier-free theories of word equations, arithmetic over length constraints, and language membership predicates for the classes of regular, visibly…
In this paper we study the class of so-called privileged words which have been previously considered only a little. We develop the basic properties of privileged words, which turn out to share similar properties with palindromes. Privileged…
We investigate the correspondence between the time and space recognition complexity of languages. For this purpose, we will code the long-continued computations of deterministic two-tape Turing machines by the relatively short-length…
Complexity of patterns is a key information for human brain to differ objects of about the same size and shape. Like other innate human senses, the complexity perception cannot be easily quantified. We propose a transparent and universal…
This paper surveys the field of quantum communication complexity. Some interesting recent results are collected concerning relations to classical communication, lower bound methods, one-way communication, and applications of quantum…