AUTOR: Kumiko Tanaka-Ishii AFILIACJA: Graduate School of Information Science and Electrical Engineering, Kyushu University TYTUŁ: Computational Constancy Measures of Texts STRESZCZENIE: In this talk, I will mainly speak about a mathematical and empirical verification of computational constancy measures for natural language text. A constancy measure characterizes a given text by having an invariant value for any size larger than a certain amount. The study of such measures has a 70-year history dating back to Yule's K, with the original intended application of author identification. We examine various measures proposed since Yule and reconsider reports made so far, thus overviewing the study of constancy measures. We then explain how K is essentially equivalent to an approximation of the second-order R'enyi entropy, thus indicating its signification within language science. We then empirically examine constancy measure candidates within this new, broader context. The approximated higher-order entropy exhibits stable convergence across different languages and kinds of text. We also show, however, that it cannot identify authors, contrary to Yule's intention. Lastly, we apply K to two unknown scripts, of the Voynich manuscript and Rongorongo, and show how the results support previous hypotheses about these scripts. AUTOR: Łukasz Dębowski AFILIACJA: Institute of Computer Science, Polish Academy of Sciences TYTUŁ: Hilberg's Hypothesis---Experimental Verification and Theoretical Results STRESZCZENIE: May generation of texts in natural language be described by a probabilistic model? Researchers from several domains worked on this problem. The theoretical difficulties inspired a few important concepts in applied mathematics, such as Markov chains, entropy, fractals, and algorithmic complexity. Hilberg's conjecture is yet another mathematical model for natural language. According to this hypothesis, the entropy of texts in natural language grows as a power law. We will review the history of empirical verification of this hypothesis and we will sketch some mathematical developments which provide its rational support. Briefly speaking, the following empirical observations support Hilberg's conjecture: estimates of entropy by Shannon using the guessing method (upper and lower bound), scaling of compression rate for universal codes (upper bound), and scaling of subword complexity and maximal repetition (lower bound). As for the theoretical results, there are three main developments. First, considerations concerning maximal repetition indicate that universal codes such as the Lempel-Ziv code may fail to efficiently compress sources that satisfy Hilberg's conjecture. Second, Hilberg's conjecture implies the empirically observed power-law growth of vocabulary in texts. Third, Hilberg's conjecture can be explained by a hypothesis that texts describe consistently an infinite random object, such as the external world.