{"title":"佩特里网","authors":"Jiacun Wang, William Tepfenhart","doi":"10.1201/9780429184185-8","DOIUrl":null,"url":null,"abstract":"Exercise 1 (Dickson’s Lemma). A quasi-order (A,≤) is a set A endowed with a reflexive and transitive ordering relation ≤. A well quasi order (wqo) is a quasi order (A,≤) s.t., for any infinite sequence a0a1 · · · in Aω, there exist indices i < j with ai ≤ aj . 1. Let (A,≤) be a wqo and B ⊆ A. Show that (B,≤) is a wqo. 2. Show that (N ] {ω},≤) is a wqo. 3. Let (A,≤) be a wqo. Show that any infinite sequence a0a1 · · · in Aω embeds an infinite increasing subsequence ai0 ≤ ai1 ≤ ai2 ≤ · · · with i0 < i1 < i2 < · · · .","PeriodicalId":195915,"journal":{"name":"Formal Methods in Computer Science","volume":"83 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Petri Nets\",\"authors\":\"Jiacun Wang, William Tepfenhart\",\"doi\":\"10.1201/9780429184185-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Exercise 1 (Dickson’s Lemma). A quasi-order (A,≤) is a set A endowed with a reflexive and transitive ordering relation ≤. A well quasi order (wqo) is a quasi order (A,≤) s.t., for any infinite sequence a0a1 · · · in Aω, there exist indices i < j with ai ≤ aj . 1. Let (A,≤) be a wqo and B ⊆ A. Show that (B,≤) is a wqo. 2. Show that (N ] {ω},≤) is a wqo. 3. Let (A,≤) be a wqo. Show that any infinite sequence a0a1 · · · in Aω embeds an infinite increasing subsequence ai0 ≤ ai1 ≤ ai2 ≤ · · · with i0 < i1 < i2 < · · · .\",\"PeriodicalId\":195915,\"journal\":{\"name\":\"Formal Methods in Computer Science\",\"volume\":\"83 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-06-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Formal Methods in Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1201/9780429184185-8\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Formal Methods in Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1201/9780429184185-8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Exercise 1 (Dickson’s Lemma). A quasi-order (A,≤) is a set A endowed with a reflexive and transitive ordering relation ≤. A well quasi order (wqo) is a quasi order (A,≤) s.t., for any infinite sequence a0a1 · · · in Aω, there exist indices i < j with ai ≤ aj . 1. Let (A,≤) be a wqo and B ⊆ A. Show that (B,≤) is a wqo. 2. Show that (N ] {ω},≤) is a wqo. 3. Let (A,≤) be a wqo. Show that any infinite sequence a0a1 · · · in Aω embeds an infinite increasing subsequence ai0 ≤ ai1 ≤ ai2 ≤ · · · with i0 < i1 < i2 < · · · .
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