We aim to generalize Büchi’s fundamental theorem on the coincidence of recognizable and MSO-definable languages to a weighted timed setting. For this, we investigate weighted timed automata and show how we can extend Wilke’s relative distance logic with weights taken from an arbitrary semiring. We show that every formula in our logic can effectively be transformed into a weighted timed automato...

Our goal is to study the complexity of infinite binary recursive sequences. We introduce several measures of the quantity of information they contain. Some measures are based on size of programs that generate the sequence, the others are based on the Kolmogorov complexity of its finite prefixes. The relations between these complexity measures are established. The most surprising among them are ...

This paper surveys two related lines of research: Logical characterizations of (non-deterministic) linear time complexity classes, and non-expressibility results concerning sublogics of existential second-order logic. Starting from Fagin's fundamental work there has been steady progress in both elds with the eeect that the weakest logics that are used in characterizations of linear time complex...

The main factor of intelligence is defined as the ability to comprehend, formalising this ability with the help of new constructs based on descriptional complexity. The result is a comprehension test, or C-test, which is exclusively defined in computational terms. Due to its absolute and non-anthropomorphic character, it is equally applicable to both humans and non-humans. Moreover, it correlat...

The descriptive complexity of a problem is the complexity of describing the problem in some logical formalism. One of the few techniques for proving separation results in descriptive complexity is to make use of games on graphs played between two players, called the spoiler and the duplicator. There are two types of these games, which differ in the order in which the spoiler and duplicator make...

In this paper we show that C-k(X), the set of continuous, realvalued functions on X topologized by the pointwise convergence topology, can have arbitrarily high Borel or projective complexity in Rx even when X is a countable regular space with a unique limit point. In addition we show how to construct countable regular spaces X for which C-n(X) lies nowhere in the projective hierarchy of the co...

In the early days of the development of model theory it was considered natural and was certainly beneficial to assume that the theories under investigation were in a countable language. The primary advantage of this assumption was the presence of the Omitting Types Theorem of Grzegorczyk, Mostowski, and Ryll-Nardzewski [1], which generalized arguments of Henkin [3] and Orey [8]. Following this,...