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 $.

中文翻译：

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使用石头和随机数传感器绕过迷宫的概率方法

在本文中，Ajans 的论文中提出的一些悬而未决的问题将继续得到解决：在石头和标志子空间存在的情况下，使用整数空间随机位生成器的机器人绕过。这项工作致力于使用带有随机位生成器的有限状态机绕过迷宫。这项任务是通过各种有限状态机绕过迷宫的快速发展主题的一部分。或者他们的团队，这与计算复杂性理论和概率论中的问题密切相关。在本文中，展示了具有随机位生成器和石头的机器人在多大维度上可以绕过带有标志子空间的整数空间。在本文中，我们将研究带有随机位生成器的有限状态机在整数空间上的行为。特别是，证明机器人绕过了$\zs^2$，不能绕过$\zs^3$；有石头的机器人绕过$\zs^4$，不能绕过$\zs^5$；有石头和旗帜的机器人绕过$\zs^6$，不能绕过$\zs^7$；一个有石头和一面旗帜的机器人绕过$\zs^8$，不能绕过$\zs^9$。