On the Simon's Congruence Neighborhood of Languages

초록

Given an integer k, Simon's congruence relation says that two strings u and v are similar to k-congruent if they have the same set of subsequences of length at most k. We extend Simon's congruence to languages. First, we define the Simon's congruence neighborhood of a language L to be a set of strings that have a similar to k-congruent string in L. Next, we define two languages L-1 and L-2 to be equivalent to(k)-congruent if both have the same Simon's congruence neighborhood. We prove that it is PSPACE-complete to check equivalent to(k)-congruence of two regular languages and decidable up to recursive languages. Moreover, we tackle the problem of computing the maximum k that makes two given languages equivalent to(k)-congruent. This problem is PSPACE-complete for two regular languages, and undecidable for context-free languages.

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