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Dissertation
Hybrid Branching-Time Logics
(2019)
We introduce and study an extension of the well-known and well-studied branching-time logics CTL, CTL+, FCTL+, CTL* and the modal μ-calculus with the so called "hybrid framework". This framework borrows ideas from first-order logic to enable more precise "structural" reasoning which is known to be impossible in the original logics. In particular, the extension with this framework enables these logics to uniquely name, reference and test for certain states, similarly to the concepts of variables and constants in ...
Dissertation
Buffered Simulation for Büchi Automata
(2019)
Wir stellen eine neue Familie von Simulationsrelationen zwischen zwei nicht deterministischen Büchi Automaten (NBA), genannt gepufferte Simulation vor. Wir erweitern das Spiel-Framework der üblichen fairen Simulation, so dass Duplicator ihren Spielzug überspringen und die Buchstaben, die Spoiler gelesenen hat, vorübergehend in einem Puffer speichern kann. Duplicator kann diese Buchstaben in ihrer Struktur dann später ausführen. Duplicator hat damit eine Vorschau in die Bewegungen von Spoiler und somit mehr Chancen, ...
Dissertation
Extremal Fixpoints for Higher-Order Modal Logic
(2018-10)
In this dissertation, we investigate the interplay between extremal fixpoints and higher-order constructs. The main Focus here is Higher-Order Modal Fixpoint Logic (HFL), an extension of the modal mu-calculus by a simply typed lambda calculus. The resulting logic is very expressive, yet the interplay of its components has not been systematically investigated so far. Goal of this thesis is to characterize the interplay of the components of HFL.
A first characterization is given by converting the denotational semantics ...