{"title":"HOM问题是EXPTIME-Complete","authors":"Carles Creus, Adrià Gascón, Guillem Godoy, Lander Ramos","doi":"10.1109/LICS.2012.36","DOIUrl":null,"url":null,"abstract":"The HOM problem questions whether the image of a given regular tree language through a given tree homomorphism is also regular. Decidability of HOM is an important theoretical question which was open for a long time. Recently, HOM has been proved decidable with a triple exponential time algorithm. In this paper we obtain an exponential time algorithm for this problem, and conclude that it is EXPTIME-complete. The proof builds upon previous results and techniques on tree automata with constraints.","PeriodicalId":407972,"journal":{"name":"2012 27th Annual IEEE Symposium on Logic in Computer Science","volume":"12 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2012-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":"{\"title\":\"The HOM Problem is EXPTIME-Complete\",\"authors\":\"Carles Creus, Adrià Gascón, Guillem Godoy, Lander Ramos\",\"doi\":\"10.1109/LICS.2012.36\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The HOM problem questions whether the image of a given regular tree language through a given tree homomorphism is also regular. Decidability of HOM is an important theoretical question which was open for a long time. Recently, HOM has been proved decidable with a triple exponential time algorithm. In this paper we obtain an exponential time algorithm for this problem, and conclude that it is EXPTIME-complete. The proof builds upon previous results and techniques on tree automata with constraints.\",\"PeriodicalId\":407972,\"journal\":{\"name\":\"2012 27th Annual IEEE Symposium on Logic in Computer Science\",\"volume\":\"12 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-06-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2012 27th Annual IEEE Symposium on Logic in Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/LICS.2012.36\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2012 27th Annual IEEE Symposium on Logic in Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/LICS.2012.36","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The HOM problem questions whether the image of a given regular tree language through a given tree homomorphism is also regular. Decidability of HOM is an important theoretical question which was open for a long time. Recently, HOM has been proved decidable with a triple exponential time algorithm. In this paper we obtain an exponential time algorithm for this problem, and conclude that it is EXPTIME-complete. The proof builds upon previous results and techniques on tree automata with constraints.
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