We prove that a group has word problem that is a growing context-sensitive language precisely if its word problem can be solved using a non-deterministic Cannon's algorithm (the deterministic algorithms being defined by Goodman and Shapiro in [6]). We generalize results of [6] to find many examples of groups not admitting non-deterministic Cannon's algorithms. This adds to the examples of Kambites and Otto in [7] of groups separating context-sensitive and growing context-sensitive word problems, and provides a new language-theoretic separation result.

中文翻译：

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存在和不存在日益严重的上下文敏感词问题的群体

我们证明，如果可以使用非确定性 Cannon 算法（古德曼和夏皮罗在 [6] 中定义的确定性算法）解决一个群体的单词问题，那么该组的单词问题是一种不断增长的上下文敏感语言。我们概括 [6] 的结果以找到许多不承认非确定性 Cannon 算法的组的示例。这增加了 [7] 中的 Kambites 和 Otto 的示例，将上下文敏感的和不断增长的上下文敏感词问题的组分开，并提供了一个新的语言理论分离结果。