Search results for " general works"
showing 4 items of 14 documents
Anti-powers in infinite words
2018
In combinatorics of words, a concatenation of $k$ consecutive equal blocks is called a power of order $k$. In this paper we take a different point of view and define an anti-power of order $k$ as a concatenation of $k$ consecutive pairwise distinct blocks of the same length. As a main result, we show that every infinite word contains powers of any order or anti-powers of any order. That is, the existence of powers or anti-powers is an unavoidable regularity. Indeed, we prove a stronger result, which relates the density of anti-powers to the existence of a factor that occurs with arbitrary exponent. As a consequence, we show that in every aperiodic uniformly recurrent word, anti-powers of ev…
The Fluted Fragment with Transitivity
2019
We study the satisfiability problem for the fluted fragment extended with transitive relations. We show that the logic enjoys the finite model property when only one transitive relation is available. On the other hand we show that the satisfiability problem is undecidable already for the two-variable fragment of the logic in the presence of three transitive relations.
A New Class of Searchable and Provably Highly Compressible String Transformations
2019
The Burrows-Wheeler Transform is a string transformation that plays a fundamental role for the design of self-indexing compressed data structures. Over the years, researchers have successfully extended this transformation outside the domains of strings. However, efforts to find non-trivial alternatives of the original, now 25 years old, Burrows-Wheeler string transformation have met limited success. In this paper we bring new lymph to this area by introducing a whole new family of transformations that have all the "myriad virtues" of the BWT: they can be computed and inverted in linear time, they produce provably highly compressible strings, and they support linear time pattern search direc…
Feature Extractors for Describing Vehicle Routing Problem Instances
2016
The vehicle routing problem comes in varied forms. In addition to usual variants with diverse constraints and specialized objectives, the problem instances themselves – even from a single shared source - can be distinctly different. Heuristic, metaheuristic, and hybrid algorithms that are typically used to solve these problems are sensitive to this variation and can exhibit erratic performance when applied on new, previously unseen instances. To mitigate this, and to improve their applicability, algorithm developers often choose to expose parameters that allow customization of the algorithm behavior. Unfortunately, finding a good set of values for these parameters can be a tedious task that…