Related papers: Defining Complexity: A Commentary to a paper by Ch…
Measuring a document's complexity level is an open challenge, particularly when one is working on a diverse corpus of documents rather than comparing several documents on a similar topic or working on a language other than English. In this…
The theory of actual causality, defined by Halpern and Pearl, and its quantitative measure - the degree of responsibility - was shown to be extremely useful in various areas of computer science due to a good match between the results it…
Scientific text is complex as it contains technical terms by definition. Simplifying such text for non-domain experts enhances accessibility of innovation and information. Politicians could be enabled to understand new findings on topics on…
The first section starts with the basic definitions following mainly the notations of the book written by E. Kushilevitz and N. Nisan. At the end of the first section I examine tree-balancing. In the second section I summarize the…
If an infinite non-periodic word is uniformly recurrent or is of bounded repetition, then the limit of its periodicity complexity is infinity. Moreover, there are uniformly recurrent words with the periodicity complexity arbitrarily high at…
Providing an abstract representation of natural and human complex structures is a challenging problem. Accounting for the system heterogenous components while allowing for analytical tractability is a difficult balance. Here I introduce…
One approach to confronting computational hardness is to try to understand the contribution of various parameters to the running time of algorithms and the complexity of computational tasks. Almost no computational tasks in real life are…
This survey describes, at an introductory level, the algebraic complexity framework originally proposed by Leslie Valiant in 1979, and some of the insights that have been obtained more recently.
An algorithm for answering conjunctive queries over SHIQ knowledge bases that is coNP in data complexity is given. The algorithm is based on the tableau algorithm for reasoning with individuals in SHIQ. The blocking conditions of the…
We study the build up of complexity on the example of 1 kg matter in different forms. We start on the simplest example of ideal gases, and then continue with more complex chemical, biological, life and social and technical structures. We…
This note discusses the paper "Penalising model component complexity" by Simpson et al. (2017). While we acknowledge the highly novel approach to prior construction and commend the authors for setting new-encompassing principles that will…
Weighted knowledge bases for description logics with typicality under a "concept-wise" multi-preferential semantics provide a logical interpretation of MultiLayer Perceptrons. In this context, Answer Set Programming (ASP) has been shown to…
In this note, we leverage some of our results from arXiv:1706.06319 to produce a concise and rigorous proof for the complexity of the generalized MinRank Problem in the under-defined and well-defined case. Our main theorem recovers and…
This habilitation thesis is intended to be a good introduction to enumeration, the problem of listing solutions. It focuses on the different ways of measuring complexity in enumeration, with a particular emphasis on my contributions to the…
While "complexity science" has achieved significant successes in several interdisciplinary fields such as economics and biology, it is only a very recent observation that legal systems -- from the way legal texts are drafted and connected…
Understanding inferences and answering questions from text requires more than merely recovering surface arguments, adjuncts, or strings associated with the query terms. As humans, we interpret sentences as contextualized components of a…
The LMC-complexity introduced by Lopez-Ruiz, Mancini and Calbet [Phys. Lett. A 209, 321-326 (1995)] is calculated for different physical situations: one instance of classical statistical mechanics, normal and exponential distributions, and…
We introduce higher simplicial complexity of a simplicial complex $K$ and higher combinatorial complexity of a finite space $P$ (i.e. $P$ is a finite poset). We relate higher simplicial complexity with higher topological complexity of $|K|$…
We initiate a study of the complexity of quantum field theories (QFTs) by proposing a measure of information contained in a QFT and its observables. We show that from minimal assertions, one is naturally led to measure complexity by two…
The 75th anniversary of Turing's seminal paper and his centennial year anniversary occur in 2011 and 2012, respectively. It is natural to review and assess Turing's contributions in diverse fields in the light of new developments that his…