{"title":"集函数增广的嵌套关系演算的内蕴表达能力的二分法和幂集算子","authors":"L. Wong","doi":"10.1145/2463664.2463670","DOIUrl":null,"url":null,"abstract":"The extensional aspect of expressive power---i.e., what queries can or cannot be expressed---has been the subject of many studies of query languages. Paradoxically, although efficiency is of primary concern in computer science, the intensional aspect of expressive power---i.e., what queries can or cannot be implemented efficiently---has been much neglected. Here, we discuss the intensional expressive power of NRC(Q, +, ·, , ÷, Σ, powerset), a nested relational calculus augmented with aggregate functions and a powerset operation. We show that queries on structures such as long chains, deep trees, etc. have a dichotomous behaviour: Either they are already expressible in the calculus without using the powerset operation or they require at least exponential space. This result generalizes in three significant ways several old dichotomy-like results, such as that of Suciu and Paredaens that the complex object algebra of Abiteboul and Beeri needs exponential space to implement the transitive closure of a long chain. Firstly, a more expressive query language---in particular, one that captures SQL---is considered here. Secondly, queries on a more general class of structures than a long chain are considered here. Lastly, our proof is more general and holds for all query languages exhibiting a certain normal form and possessing a locality property.","PeriodicalId":92118,"journal":{"name":"Proceedings of the ... ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems. ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems","volume":"11 1","pages":"285-296"},"PeriodicalIF":0.0000,"publicationDate":"2013-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"A dichotomy in the intensional expressive power of nested relational calculi augmented with aggregate functions and a powerset operator\",\"authors\":\"L. Wong\",\"doi\":\"10.1145/2463664.2463670\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The extensional aspect of expressive power---i.e., what queries can or cannot be expressed---has been the subject of many studies of query languages. Paradoxically, although efficiency is of primary concern in computer science, the intensional aspect of expressive power---i.e., what queries can or cannot be implemented efficiently---has been much neglected. Here, we discuss the intensional expressive power of NRC(Q, +, ·, , ÷, Σ, powerset), a nested relational calculus augmented with aggregate functions and a powerset operation. We show that queries on structures such as long chains, deep trees, etc. have a dichotomous behaviour: Either they are already expressible in the calculus without using the powerset operation or they require at least exponential space. This result generalizes in three significant ways several old dichotomy-like results, such as that of Suciu and Paredaens that the complex object algebra of Abiteboul and Beeri needs exponential space to implement the transitive closure of a long chain. Firstly, a more expressive query language---in particular, one that captures SQL---is considered here. Secondly, queries on a more general class of structures than a long chain are considered here. Lastly, our proof is more general and holds for all query languages exhibiting a certain normal form and possessing a locality property.\",\"PeriodicalId\":92118,\"journal\":{\"name\":\"Proceedings of the ... ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems. ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems\",\"volume\":\"11 1\",\"pages\":\"285-296\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2013-06-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the ... ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems. 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A dichotomy in the intensional expressive power of nested relational calculi augmented with aggregate functions and a powerset operator
The extensional aspect of expressive power---i.e., what queries can or cannot be expressed---has been the subject of many studies of query languages. Paradoxically, although efficiency is of primary concern in computer science, the intensional aspect of expressive power---i.e., what queries can or cannot be implemented efficiently---has been much neglected. Here, we discuss the intensional expressive power of NRC(Q, +, ·, , ÷, Σ, powerset), a nested relational calculus augmented with aggregate functions and a powerset operation. We show that queries on structures such as long chains, deep trees, etc. have a dichotomous behaviour: Either they are already expressible in the calculus without using the powerset operation or they require at least exponential space. This result generalizes in three significant ways several old dichotomy-like results, such as that of Suciu and Paredaens that the complex object algebra of Abiteboul and Beeri needs exponential space to implement the transitive closure of a long chain. Firstly, a more expressive query language---in particular, one that captures SQL---is considered here. Secondly, queries on a more general class of structures than a long chain are considered here. Lastly, our proof is more general and holds for all query languages exhibiting a certain normal form and possessing a locality property.