A family of logics for expressing patterns in sequences is investigated. The logics are all fragments of first-order logic, but they are variable-free. Instead, they can use substring and subsequence constraints as basic propositions. Propositions expressing constraints on the beginning or the end of the sequence are also available. Also wildcards can be used, which is important when the alphabet is not fixed, as is typical in database applications. The maximal logic with all four features of substring, subsequence, begin–end constraints, and wildcards, turns out to be equivalent to the family of star-free regular languages of dot-depth at most one. We investigate the lattice formed by taking all possible combinations of the above four features, and show it to be strict. For instance, we formally confirm what might intuitively be expected, namely, that boolean combinations of substring constraints are not sufficient to express subsequence constraints, and vice versa. We show an expressiveness hierarchy results from allowing multiple wildcards. We also investigate what happens with regular expressions when concatenation is replaced by subsequencing. Finally, we study the expressiveness of our logic relative to first-order logic.

中文翻译：

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序列模式语言中的子序列与子字符串约束

研究了一系列用于表达序列模式的逻辑。这些逻辑都是一阶逻辑的片段，但它们是无变量的。相反，他们可以使用子串和子序列约束作为基本命题。表达对序列开头或结尾的约束的命题也是可用的。还可以使用通配符，这在字母表不固定时很重要，这在数据库应用程序中很常见。具有子串、子序列、开始-结束约束和通配符所有四个特征的最大逻辑结果证明最多相当于一个点深度的无星号正则语言家族。我们研究了通过采用上述四个特征的所有可能组合形成的格子，并证明它是严格的。例如，我们正式确认可能直觉上预期的内容，即，子串约束的布尔组合不足以表达子序列约束，反之亦然。我们展示了允许多个通配符的表现力层次结构。我们还研究了当串联被子序列取代时正则表达式会发生什么。最后，我们研究我们的逻辑相对于一阶逻辑的表达能力。