On Continuous Nondeterminism and State Minimality

Harmonicity and Minimality of Vector Fields on Lorentzian Lie Groups

‎We consider four-dimensional lie groups equipped with‎ ‎left-invariant Lorentzian Einstein metrics‎, ‎and determine the harmonicity properties ‎of vector fields on these spaces‎. ‎In some cases‎, ‎all these vector fields are critical points for the energy functional ‎restricted to vector fields‎. ‎We also classify vector fields defining harmonic maps‎, ‎and calculate explicitly the energy of t...

Delayed Nondeterminism in Continuous-Time Markov Decision Processes

Schedulers in randomly timed games can be classified as to whether they use timing information or not. We consider continuous-time Markov decision processes (CTMDPs) and define a hierarchy of positional (P) and historydependent (H) schedulers which induce strictly tighter bounds on quantitative properties on CTMDPs. This classification into time abstract (TA), total time (TT) and fully time-dep...

Reasoning about programs combining probability and nondeterminism in a probabilistic logic over continuous state spaces

Discrete abstraction and supervisory control of switching systems

In this paper we propose a method to create discrete abstraction of state space behavior for continuous-time systems based on gradient analysis of the system dynamics. Then we describe how to use such a discrete model to design a supervisory controller for a given safety spiflication for the system. Finally we provide an entropy measure of nondeterminism, which can be used to evaluate the quali...

Stochastic Nondeterminism and Effectivity Functions

This paper investigates stochastic nondeterminism by relating nondeterministic labelled Markov processes and stochastic effectivity functions to each other; the underlying state spaces are continuous. Both generalizations to labelled Markov transition systems have been proposed recently with differing intentions. It turns out that they display surprising similarities and interesting differences...