A new distance function for fuzzy sets is introduced. It is based on the descriptive complexity, that is, the number of bits (on average) that are needed to describe an element in the symmetric difference of the two sets. The value of the distance gives the amount of additional information needed to describe either one of the two sets when the other is known. We prove that the distance function...

Using ideas from synthetic topology, a new approach to descriptive set theory is suggested. Synthetic descriptive set theory promises elegant explanations for various phenomena in both classic and effective descriptive set theory. Presently, we mainly focus on developing the ideas in the category of represented spaces.

Symport/antiport P systems provide a very simple machinery inspired by corresponding operations in the living cell. It turns out that systems of small descriptional complexity are needed to achieve the universality by these systems. This makes them a good candidate for small universal devices replacing register machines for different simulations, especially when a simulating parallel machinery ...

In recent years the study of probabilistic transition systems has shifted to transition relations over distributions to allow for a smooth adaptation of the standard non-probabilistic apparatus. In this paper we study transition relations over probability distributions in a setting with internal actions. We provide new logics that characterize probabilistic strong, weak and branching bisimulati...

We give some sufficient conditions under which any valued field that admits quantifier elimination in the Macintyre language is henselian. Then, without extra assumptions, we prove that if a valued field of characteristic (0, 0) has a Z-group as its value group and admits quantifier elimination in the main sort of the Denef-Pas style language LRRP then it is henselian. In fact the proof of this...

Currently, adaptive educational hypermedia systems (AEHS) are described with nonuniform methods, depending on the specific view on the system, the application, or other parameters. There is no common language for expressing functionality of AEHS, hence these systems are difficult to compare and analyze. In this paper we investigate how a logical description can be employed to characterize adapt...

Statistics is a science that provides precise techniques for collecting and sorting information made easy by tools and methods for further analysis. The object of descriptive statistics, from sample data, is to describe the most important characteristics, by which we refer to those amounts that provide information on the topic of interest which we are studying.