We make the first steps towards showing a general “randomness for free” theorem for stochastic automata. The goal of such theorems is to replace randomized schedulers by averages of pure schedulers. Here, we explore the case of measurable multifunctions and their measurable selections. This involves constructing probability measures on the measurable space of measurable selections of a given measurable multifunction, which seems to be a fairly novel problem. We then extend this to the case of IT automata, namely, non-deterministic (infinite) automata with a history-dependent transition relation. Throughout, we strive to make our assumptions minimal.
Random Measurable SelectionsHorizons of the Mind. A Tribute to Prakash Panangaden
SEGALA, Roberto
2014-01-01
Abstract
We make the first steps towards showing a general “randomness for free” theorem for stochastic automata. The goal of such theorems is to replace randomized schedulers by averages of pure schedulers. Here, we explore the case of measurable multifunctions and their measurable selections. This involves constructing probability measures on the measurable space of measurable selections of a given measurable multifunction, which seems to be a fairly novel problem. We then extend this to the case of IT automata, namely, non-deterministic (infinite) automata with a history-dependent transition relation. Throughout, we strive to make our assumptions minimal.
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