{"title":"具有状态的二维一元向量加法系统的可达性是nl完全的*","authors":"Matthias Englert, R. Lazic, Patrick Totzke","doi":"10.1145/2933575.2933577","DOIUrl":null,"url":null,"abstract":"Blondin et al. showed at LICS 2015 that two-dimensional vector addition systems with states have reachability witnesses of length exponential in the number of states and polynomial in the norm of vectors. The resulting guess-and-verify algorithm is optimal (PSPACE), but only if the input vectors are given in binary. We answer positively the main question left open by their work, namely establish that reachability witnesses of pseudo-polynomial length always exist. Hence, when the input vectors are given in unary, the improved guess-and-verify algorithm requires only logarithmic space.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"281 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2016-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"32","resultStr":"{\"title\":\"Reachability in Two-Dimensional Unary Vector Addition Systems with States is NL-Complete*\",\"authors\":\"Matthias Englert, R. Lazic, Patrick Totzke\",\"doi\":\"10.1145/2933575.2933577\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Blondin et al. showed at LICS 2015 that two-dimensional vector addition systems with states have reachability witnesses of length exponential in the number of states and polynomial in the norm of vectors. The resulting guess-and-verify algorithm is optimal (PSPACE), but only if the input vectors are given in binary. We answer positively the main question left open by their work, namely establish that reachability witnesses of pseudo-polynomial length always exist. Hence, when the input vectors are given in unary, the improved guess-and-verify algorithm requires only logarithmic space.\",\"PeriodicalId\":206395,\"journal\":{\"name\":\"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)\",\"volume\":\"281 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2016-02-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"32\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/2933575.2933577\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/2933575.2933577","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Reachability in Two-Dimensional Unary Vector Addition Systems with States is NL-Complete*
Blondin et al. showed at LICS 2015 that two-dimensional vector addition systems with states have reachability witnesses of length exponential in the number of states and polynomial in the norm of vectors. The resulting guess-and-verify algorithm is optimal (PSPACE), but only if the input vectors are given in binary. We answer positively the main question left open by their work, namely establish that reachability witnesses of pseudo-polynomial length always exist. Hence, when the input vectors are given in unary, the improved guess-and-verify algorithm requires only logarithmic space.
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