Two-dimensional general row jumping finite automata were recently introduced as an interesting computational model for accepting two-dimensional languages. These automata are nondeterministic. They guess an order in which rows of the input array are read and they jump to the next row only after reading all symbols in the previous row. In each row, they choose, also nondeterministically, an order in which segments of the row are read. In this paper, we study the membership problem for these automata. We show that each general row jumping finite automaton can be simulated by a nondeterministic Turing machine with space bounded by the logarithm. This means that the fixed membership problems for such automata are in NL, and so in P. On the other hand, we show that the uniform membership problem is NP-complete.

中文翻译：

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二维一般跳行有限自动机的隶属问题

最近引入了二维通用跳行有限自动机作为一种有趣的计算模型，用于接受二维语言。这些自动机是不确定的。他们猜测输入数组的行被读取的顺序，并且只有在读取前一行中的所有符号后才跳转到下一行。在每一行中，它们也不确定地选择读取行段的顺序。在本文中，我们研究了这些自动机的隶属问题。我们证明了每个一般的跳行有限自动机都可以通过一个非确定性的图灵机来模拟，其空间以对数为界。这意味着这种自动机的固定隶属问题在 NL 中，因此在 P 中。另一方面，我们证明了统一隶属问题是 NP 完全的。