Universality and Almost Decidability

What's Decidable about Weighted Automata?

Weighted automata map input words to numerical values. Applications of weighted automata include formal verification of quantitative properties, as well as text, speech, and image processing. In the 90’s, Krob studied the decidability of problems on rational series, which strongly relate to weighted automata. In particular, it follows from Krob’s results that the universality problem (that is, ...

On Büchi One-Counter Automata

Equivalence of deterministic pushdown automata is a famous problem in theoretical computer science whose decidability has been shown by Sénizergues. Our first result shows that decidability no longer holds when moving from finite words to infinite words. This solves an open problem that has recently been raised by Löding. In fact, we show that already the equivalence problem for deterministic B...

Dynamics, Information and Computation

Structure of the thesis The heart of this thesis is composed of four independent chapters, related by a common flavor of systems theory and computer science. Chapter 3: Almost periodic configurations and undecidable dynamics. We describe Turing machines, tilings and infinite words as dynamical systems and analyze some of their dynamical properties. It is known that some of these systems do not ...

Decidability and Tameness in the Theory of Finite Semigroups

On the Undecidability of Universality for Timed Automata with Minimal Resources

In 1994 Alur and Dill introduced timed automata and showed that universality was undecidable there. Since then it has been shown that under certain restrictions the problem becomes decidable. But the frontier between decidability and undecidability is still vast. We aim at narrowing this gap considerably. Our main accomplishment is to prove that universality stays undecidable over weakly monoto...