Well-Quasi-Ordering, Overview and its Applications
نویسنده
چکیده
This talk shows theorems, techniques, and applications of well-quasi-ordering (WQO). First, we introduce what is WQO, and Kruskaltype theorems on various data structures [31, 15, 16, 23, 34, 33]. The basic proof technique, minimal bad sequence (MBS), will be introduced for the simplest case, Higman’s Lemma. Then, WQO will be extended to better-quasi-ordering (BQO) for infinite data structures [31, 25, 24, 26, 18, 36, 39]. The variation with the gap-condition will be also mentioned [37, 17, 12, 13, 40]. Second, the relation between WQO and regularity will be discussed. The basic fact is that a set of finite words is regular if, and only if, it is upward-closed wrt some WQO on finite words [8]. Its variations are also mentioned [14, 5, 28]. Based on these theoretical results, we overview applications of WQO techniques:
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