Related papers: Effective complexity of stationary process realiza…
This thesis is concerned with investigations into the "complexity of term rewriting systems". Moreover the majority of the presented work deals with the "automation" of such a complexity analysis. The aim of this introduction is to present…
We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…
We develop a static complexity analysis for a higher-order functional language with structural list recursion. The complexity of an expression is a pair consisting of a cost and a potential. The former is defined to be the size of the…
Binary segmentation is the classic greedy algorithm which recursively splits a sequential data set by optimizing some loss or likelihood function. Binary segmentation is widely used for changepoint detection in data sets measured over space…
In resolving instances of a computational problem, if multiple instances of interest share a feature in common, it may be fruitful to compile this feature into a format that allows for more efficient resolution, even if the compilation is…
Significant work has been done on learning regular expressions from a set of data values. Depending on the domain, this approach can be very successful. However, significant time is required to learn these expressions and the resulting…
Algorithmic statistics considers the following problem: given a binary string $x$ (e.g., some experimental data), find a "good" explanation of this data. It uses algorithmic information theory to define formally what is a good explanation.…
We present an standard constraints generation algorithm to find an explicit set whose robustness is equal to the robustness of the feasible solution set of a combinatorial optimization problem with cost uncertainty. Computational experience…
In this paper we give a definition for quantum Kolmogorov complexity. In the classical setting, the Kolmogorov complexity of a string is the length of the shortest program that can produce this string as its output. It is a measure of the…
Finite-state tree automata are a well studied formalism for representing term languages. This paper studies the problem of determining the regularity of the set of instances of a finite set of terms with variables, where each variable is…
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…
The fast changing reality in technical and natural domains perceived by always more accurate observations has drawn attention on new and very broad class of systems with specific behaviour represented under the common wording complexity.…
We describe an alternative method (to compression) that combines several theoretical and experimental results to numerically approximate the algorithmic (Kolmogorov-Chaitin) complexity of all $\sum_{n=1}^82^n$ bit strings up to 8 bits long,…
We observe that successive applications of known results from the theory of positive systems lead to an {\it efficient general algorithm} for positive realizations of transfer functions. We give two examples to illustrate the algorithm, one…
We consider the communication complexity of a number of distributed optimization problems. We start with the problem of solving a linear system. Suppose there is a coordinator together with $s$ servers $P_1, \ldots, P_s$, the $i$-th of…
We propose a new type of entropic descriptor that is able to quantify the statistical complexity (a measure of complex behaviour) by taking simultaneously into account the average departures of a system's entropy S from both its maximum…
To analyze the evolutionary emergence of structural complexity in physical processes we introduce a general, but tractable, model of objects that interact to produce new objects. Since the objects--\emph{$epsilon$-machines}--have well…
This work builds on a rich discourse surrounding the social brain hypothesis as well as the definition and quantification of social complexity. We believe this manuscript provides a new perspective on the topic by pairing a conceptual…
We define the notion of localizable property for a dynamical system. Then we survey three properties of complexity and relate how they are known to be typical among differentiable dynamical systems. These notions are the fast growth of the…
Computational complexity is a core theory of computer science, which dictates the degree of difficulty of computation. There are many problems with high complexity that we have to deal, which is especially true for AI. This raises a big…