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The complexity of regex crosswords
Information and Computation ( IF 1 ) Pub Date : 2021-06-25 , DOI: 10.1016/j.ic.2021.104777
Stephen Fenner , Daniel Padé , Thomas Thierauf

In a typical regex crossword puzzle, one is given two non-empty lists R1,,Rm and C1,,Cn of regular expressions (regexes) over some alphabet, and the challenge is to fill in an m×n grid of characters such that the string formed by the ith row is in L(Ri) and the string formed by the jth column is in L(Cj), for all 1im and 1jn. We consider a restriction of this puzzle where all the Ri are equal to one another and similarly the Cj. We consider a 2-player version of this puzzle, showing it to be PSPACE-complete. Using a reduction from 3SAT, we also give a new, simple proof of the known result that the existence problem of a solution for the restricted (1-player) puzzle is NP-complete. We also prove NP-completeness where all the row and column regular expressions are equal to each other.



中文翻译:

正则表达式填字游戏的复杂性

在一个典型的正则表达式的纵横字谜,给出一个两个非空列表 电阻1,,电阻C1,,Cn 正则表达式(正则表达式)过字母表一些,而挑战是填补了 ×n 使得串所形成的字符格 一世 排在 (电阻一世) 和字符串由形成 j 列是 (Cj), 对所有人 1一世1jn. 我们认为这一难题的限制,所有的电阻一世 彼此相等,并且类似地 Cj. 我们认为这个难题的2播放器版本,显示出它是PSPACE -complete。使用减少3SAT,我们也给已知结果的一个新的,简单的证明,为限制(1人)谜题的解决方案存在的问题是NP -complete。我们也证明了NP -completeness,所有的行和列的正则表达式彼此相等。

更新日期:2021-06-28
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