{"title":"带常数的词方程在PSPACE中是可满足的","authors":"Wojciech Plandowski","doi":"10.1109/SFFCS.1999.814622","DOIUrl":null,"url":null,"abstract":"We prove that the satisfiability problem for word equations is in PSPACE. The satisfiability problem for word equations has a simple formulation: find out whether or not an input word equation has a solution. The decidability of the problem was proved by G.S. Makanin (1977). His decision procedure is one of the most complicated algorithms existing in the literature. We propose an alternative algorithm. The full version of the algorithm requires only a proof of the upper bound for index of periodicity of a minimal solution (A. Koscielski and L. Pacholski, see Journal of ACM, vol.43, no.4. p.670-84). Our algorithm is the first one which is proved to work in polynomial space.","PeriodicalId":385047,"journal":{"name":"40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"1999-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"212","resultStr":"{\"title\":\"Satisfiability of word equations with constants is in PSPACE\",\"authors\":\"Wojciech Plandowski\",\"doi\":\"10.1109/SFFCS.1999.814622\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that the satisfiability problem for word equations is in PSPACE. The satisfiability problem for word equations has a simple formulation: find out whether or not an input word equation has a solution. The decidability of the problem was proved by G.S. Makanin (1977). His decision procedure is one of the most complicated algorithms existing in the literature. We propose an alternative algorithm. The full version of the algorithm requires only a proof of the upper bound for index of periodicity of a minimal solution (A. Koscielski and L. Pacholski, see Journal of ACM, vol.43, no.4. p.670-84). Our algorithm is the first one which is proved to work in polynomial space.\",\"PeriodicalId\":385047,\"journal\":{\"name\":\"40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1999-10-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"212\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SFFCS.1999.814622\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SFFCS.1999.814622","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Satisfiability of word equations with constants is in PSPACE
We prove that the satisfiability problem for word equations is in PSPACE. The satisfiability problem for word equations has a simple formulation: find out whether or not an input word equation has a solution. The decidability of the problem was proved by G.S. Makanin (1977). His decision procedure is one of the most complicated algorithms existing in the literature. We propose an alternative algorithm. The full version of the algorithm requires only a proof of the upper bound for index of periodicity of a minimal solution (A. Koscielski and L. Pacholski, see Journal of ACM, vol.43, no.4. p.670-84). Our algorithm is the first one which is proved to work in polynomial space.
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