Random Measurable Selections

Abstract

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.

Randomness for free

“…The other impact of our characterization is as follows: for the class of games where randomization is free in transition function, future algorithmic and complexity analysis can focus on the simpler class of deterministic games; and for the class of games where randomization is free in strategies, future analysis of such games can focus on the simpler class of pure strategies. Thus our results will be useful tools for simpler analysis techniques in the study of games, as already demonstrated in [6][7][8][9]16,17].…”