Related papers: Enumeration Complexity: Incremental Time, Delay an…
This is a chapter in the Encyclopedia of Robotics. It is devoted to the study of complexity of complete (or exact) algorithms for robot motion planning. The term ``complete'' indicates that an approach is guaranteed to find the correct…
Dependence logics are a modern family of logics of independence and dependence which mimic notions of database theory. In this paper, we aim to initiate the study of enumeration complexity in the field of dependence logics and thereby get a…
The term {\em complexity} is used informally both as a quality and as a quantity. As a quality, complexity has something to do with our ability to understand a system or object -- we understand simple systems, but not complex ones. On…
This chapter presents a brief review of complexity research in mathematics education. We argue how research on complexity, as it pertains to mathematics education, can be viewed as an epistemological discourse, an historical discourse, a…
Mathematical Selection is a method in which we select a particular choice from a set of such. It have always been an interesting field of study for mathematicians. Accordingly, Combinatorial Optimization is a sub field of this domain of…
We study multivariate problems like function approximation, numerical integration, global optimization and dispersion. We obtain new results on the information complexity $n(\varepsilon,d)$ of these problems. The information complexity is…
Enumeration of tilings is the mathematical study concerning the total number of coverings of regions by similar pieces without gaps or overlaps. Enumeration of tilings has become a vibrant subfield of combinatorics with connections and…
This dissertation presents a multifaceted look into the structural decomposition of permutation classes. The theory of permutation patterns is a rich and varied field, and is a prime example of how an accessible and intuitive definition…
This is a survey on the computational complexity of nonlinear mixed-integer optimization. It highlights a selection of important topics, ranging from incomputability results that arise from number theory and logic, to recently obtained…
In this chapter, a statistical measure of complexity is introduced and some of its properties are discussed. Also, some straightforward applications are shown.
In this report, we summarize the set partition enumeration problems and thoroughly explain the algorithms used to solve them. These algorithms iterate through the partitions in lexicographic order and are easy to understand and implement in…
How best to quantify the information of an object, whether natural or artifact, is a problem of wide interest. A related problem is the computability of an object. We present practical examples of a new way to address this problem. By…
These notes are a slightly enlarged version of my habilitation thesis, where our research interest and main results in the past few years are summarized. Most of the discussion revolves around complex ordinary differential equations and…
Reasoning with defeasible and conflicting knowledge in an argumentative form is a key research field in computational argumentation. Reasoning under various forms of uncertainty is both a key feature and a challenging barrier for automated…
This paper proposes a thought experiment to search for efficient bounded algorithms of NPC problems by machine enumeration. The key contributions are: -- On Universal Turing Machines, a program's time complexity should be characterized as:…
This introductory paper is structured in the form of an "interview", where the author answers the following questions: Why did you begin working with complex systems? How would you define complexity? What is your favourite aspect/concept of…
Complexity is a multi-faceted phenomenon, involving a variety of features including disorder, nonlinearity, and self-organisation. We use a recently developed rigorous framework for complexity to understand measures of complexity. We…
A measure of complexity based on a probabilistic description of physical systems is proposed. This measure incorporates the main features of the intuitive notion of such a magnitude. It can be applied to many physical situations and to…
In this chapter, I review the main methods and techniques of complex systems science. As a first step, I distinguish among the broad patterns which recur across complex systems, the topics complex systems science commonly studies, the tools…
This article attempts to describe specific mental techniques that are related to resolving very complex tasks in software engineering. This subject may be familiar to some software specialists to different extents; however, there is…