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.

State complexity is a descriptive complexity measure for regular languages. We investigate the problems related to the state complexity of regular languages and their operations. In particular, we compare the state complexity results on regular languages with those on nite languages.

In this paper we present logical characterizations of two preorders, within the framework of Hennessy-Milner Logics. The two preorders (loosely termed bisimulation-based efficiency preorders) are on processes represented as labelled transition systems. The characterizations are particularly interesting as they explore preorders lying between strong and weak bisimilarity, guided by a principle o...

A new distance function dist (A,B) for fuzzy sets A and B is introduced. It is based on the descriptive complexity, i.e., the number of bits (on average) that are needed to describe an element in the symmetric difference of the two sets. The distance gives the amount of additional information needed to describe any one of the two sets given the other. We prove its mathematical properties and pe...

Syntactic constraints in Koskenniemi's Finite-State Intersection Grammar (FSIG) are logically less complex than their formalism (Koskenniemi et al., 1992) would suggest: It turns out that although the constraints in Voutilainen's (1994) FSIG description of English make use of several extensions to regular expressions, the description as a whole reduces to a finite combination of union, compleme...

Acknowledgements : many thanks to professor Giovanni Pighizzini for its welcome and for having directed my internship. Many thanks also to Carlo Mereghetti and Beatrice Palano and all organizing committee of NCMA workshop for having given me the possibility to assist at this workshop. Many thanks also to Viliam Geffert for his contribution to our work. Thanks to Antonio Capoduro for coffees and...

My research interests involve Finite Model Theory and Descriptive Complexity, an area of research nestled in the intersection of Combinatorics, Logic and Computer Science. Inspired by Ehrenfeucht–Fräıssé games, I have been studying local properties of regular colored graphs– in particular, the computational complexity of realizing a given set of neighborhoods in a graph.

Mathematicians in the early 20th century discovered that the Axiom of Choice implied the existence of pathological subsets of the real line lacking desirable regularity properties (for example nonmeasurable sets). This gave rise to descriptive set theory, a systematic study of classes of sets where these pathologies can be avoided, including, in particular, the definable sets. In the first half...

The Descriptive Component Display Theory describes explicitly the components of the instructional process; it dissects, identifies and summarizes learner performances; it likewise, dissects and synthesizes the subject matter content and matches content classification with learner performances. Possible presentation forms are also classified as are the modes with which these presentations can be...

Logic is playing an increasingly important role in the engineering of real-time, hybrid, and cyber-physical systems, but mostly in the form of posterior verification and high-level analysis. The core methodology in the design of real-world systems consists mainly of control theory and numerical analysis, and has remained mostly free of logic and formal approaches. As a result, besides facing ex...