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 and of regular expressions (regexes) over some alphabet, and the challenge is to fill in an grid of characters such that the string formed by the row is in and the string formed by the column is in , for all and . We consider a restriction of this puzzle where all the are equal to one another and similarly the . We consider a 2-player version of this puzzle, showing it to be PSPACE-complete. Using a reduction from , 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 和 正则表达式(正则表达式)过字母表一些,而挑战是填补了 使得串所形成的字符格 排在 和字符串由形成 列是 , 对所有人 和 . 我们认为这一难题的限制,所有的 彼此相等,并且类似地 . 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,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。