By applying descriptive set theory to the Wagner’s fine structure of regular ω-languages we get quite different proofs of his results and obtain new results. We give an automata-free description of the fine structure. We present also a simple property of a deterministic Muller automaton equivalent to the condition that the corresponding regular ω-language belongs to any given level of the fine ...

This is a proposal for a thesis in the interface of descriptive set theory and computable analysis, in a continuation of my MoL thesis [9]. There, I was interested in studying connections between game characterizations of classes of functions in descriptive set theory and the theory of Weihrauch reducibility, in particular searching for counterparts in computable analysis to the game characteri...

We consider P systems with a linear membrane structure working on objects over a unary alphabet using sets of rules resembling homomorphisms. Such a restricted variant of P systems allows for a unique minimal representation of the generated unary language and in that way for an effective solution of the equivalence problem. Moreover, we examine the descriptional complexity of unary P systems wi...

Kolmogorov complexity, which is also called algorithmic (descriptive) complexity is an object, such as a piece of text, to measure the computational resources needed, which are mostly the length of the shortest binary program to specify an object. Strings whose Kolmogorov complexity is small relative to the string’s size are not considered to be complex and easy to use a short program to specif...

Recently, it has been shown that every recursively enumerable language can be generated by a scattered context grammar with no more than three nonterminals. However, in that construction, the maximal number of nonterminals simultaneously rewritten during a derivation step depends on many factors, such as the cardinality of the alphabet of the generated language and the structure of the generate...

In this work, we present a new bottom-up algorithm for decision tree pruning that is very e cient (requiring only a single pass through the given tree), and prove a strong performance guarantee for the generalization error of the resulting pruned tree. We work in the typical setting in which the given tree T may have been derived from the given training sample S, and thus may badly over t S. In...