### February 8, 2016

**Edon Kelmendi**(LaBRI)

We study two-player stochastic games with reachability conditions where the maximizer has no information whereas the minimizer has perfect-information. The question of limit-sure reachability is the following: is it true that for all epsilon>0 and finite-memory strategies tau (for the minimizer) there exists a finite word w (for the maximizer) such that the probability of reaching the final states is larger than 1-epsilon when the game unravels according to w and tau. This question is undecidable in general, the reason being that if the minimizer has no choice at all such a game is equivalent to a probabilistic finite automaton where the value 1 problem is undecidable. Building up on previous work on probabilistic finite automata we identify a robust class of games where the limit-sure reachability is decidable. We also show that there are games where the optimal strategies of the minimizer need infinite-memory which is slightly surprising since the minimizer has perfect-information.