  In this paper, some open questions that are posed in Ajans' dissertation
continue to be addressed: a robot bypass with a generator of random bits of
integer spaces in the presence of a stone and a subspace of flags. This work is
devoted to bypassing the maze with a finite state machine with a random bit
generator. This task is part of the rapidly evolving theme of bypassing the
maze by various finite state machines. or their teams, which is closely related
to problems from the theory of computational complexity and probability theory.
In this paper, it is shown at what dimensions a robot with a random bit
generator and a stone can bypass integer space with a subspace of flags. In
this paper, we will study the behavior of a finite state machine with a random
bit generator on integer spaces. In particular, it was proved that the robot
bypasses $ \ zs ^ 2 $ and cannot bypass $ \ zs ^ 3 $; a robot with a stone
bypasses $ \ zs ^ 4 $ and cannot bypass $ \ zs ^ 5 $; a robot with a stone and
a flag bypasses $ \ zs ^ 6 $ and cannot bypass $ \ zs ^ 7 $; a robot with a
stone and a plane of flags bypasses $ \ zs ^ 8 $ and cannot bypass $ \ zs ^ 9
$.
