Separability by Short Subsequences and Subwords

The separability problem for regular languages asks, given two regular languages I and E, whether there exists a language S that separates the two, that is, includes I but contains nothing from E. Typically, S comes from a simple, less expressive class of languages than I and E. In general, a simple separator $S$ can be seen as an approximation of I or as an explanation of how I and E are different. In a database context, separators can be used for explaining the result of regular path queries or for finding explanations for the difference between paths in a graph database, that is, how paths from given nodes u_1 to v_1 are different from those from u_2 to v_2. We study the complexity of separability of regular languages by combinations of subsequences or subwords of a given length k. The rationale is that the parameter k can be used to influence the size and simplicity of the separator. The emphasis of our study is on tracing the tractability of the problem.

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