+********************************************************************** * * *                          Einladung * * * *                     Informatik-Oberseminar * * * +********************************************************************** Zeit:  Freitag, 20. Juni 2025, 09:00 Uhr Ort:   Raum 9222 (Informatikzentrum E3, Ahornstraße 55) Referent: Lutz Klinkenberg, M.Sc.                   Lehrstuhl für Informatik 2 Thema: Analysis of Probabilistic Programs Using Generating Functions Abstract: Probabilistic programming languages have emerged as a powerful tool for modeling complex and uncertain systems. Widely applied in fields like artificial intelligence, machine learning, robotics but also in non-technical domains as, e.g., healthcare, social and climate sciences, economic and psychology, these languages allow us to succinctly represent probabilistic processes, including those involving loops, recursion, and other intricate structures. However, reasoning about such programs, particularly those with infinite loops or non- terminating behavior, poses significant challenges. This dissertation introduces a novel approach to address these challenges by developing a denotational probability generating function (PGF) semantics for discrete probabilistic programs with loops. This semantics provides an exact and compact representation of program behaviors, enabling exact Bayesian inference where prior methods often relied on approximations. A central contribution of this work is the introduction of invariant-based reasoning techniques, which facilitate the systematic derivation of posterior distributions and hence also properties like expectations and higher-order moments, even for possibly unbounded loops. Furthermore, we present a syntactic characterization of a class of proba- bilistic programs for which the distributions they describe can be expressed as rational closed-form generating functions. This characterization ensures that exact inference is preserved within this class, allowing for efficient alge- braic manipulation and direct computation of quantities such as tail bounds and moments. By linking program syntax to the algebraic tractability of their semantics, this work establishes a foundational framework for exact reasoning in probabilistic programming. This framework not only enhances the capacity for exact Bayesian inference enabling decision-making under uncertainty but also broadens the applicability of probabilistic programming to domains where formal verification is inevitable. It combines theoretical rigor with practical utility, offering a unified perspective on the structure and behavior of discrete probabilistic programs. Es laden ein: die Dozentinnen und Dozenten der Informatik