T. Hirst and D. Harel, Completeness Results for Recursive Databases, Journal of Computer and System Sciences, to appear. (Also: 12th ACM Symp. on Principles of Database Systems (1993), 244--252.)  Home/Search   Document Details and Download   Summary   Related Articles   Check

....General results on the com Work supported in part by Esprit Project BRA AMUSING. Work supported in part by NSF grants IRI 9109520 and IRI 9117094. A part of work was done while visiting I.N.R.I.A. pleteness of query languages for infinite recursive databases were reported by Hirst and Harel in [HH93], where two classes of recursive databases are considered, and it is shown that: i) quantifier free first order logic is complete on the class of all recursive databases, and (ii) a version of Chandra and Harel s QL [CH80] is complete on highly symmetric databases. In this paper, we consider ....

T. Hirst and D. Harel. Completeness results of recursive data bases. In Proc. 12th ACM Symp. on Principles of Database Systems, pages 244--252, 1993.

....69978, Israel, milo math.tau.ac.il x Department of Computer Science, The Hebrew University, Jerusalem 91904, Israel, paula cs.huji.ac.il model, the data types used in instances of a data model, and queries. Several recent papers have indicated the role of having different notions of genericity [9, 13]. On a more pragmatic level, genericity can be used as a tool for proving inexpressibility results: If one shows that all queries in a language are of a certain genericity class, then queries not in the class are not expressible. We follow Chandra [6] in presenting a few such results. Also, we ....

T. Hirst and D. Harel. Completeness results for recursive databases. In PODS, 1993.

....6.3 Aggregate and arithmetic operators Aggregate operators [33] and arithmetic operators [104] have been added to logic programming and deductive databases in order to make the language more expressive. Harel discusses recursive languages, which are a generalization of languages with arithmetic [51]. In this section we describe how arithmetic and aggregate operators can be included in Gulog. Again we consider only positive programs. Aggregate atoms and arithmetic operators are allowed in the body of a clause. We illustrate the use of an aggregate atom in the following example. Example ....

D. Harel and T. Hirst. Completeness results for recursive data bases. In Proceedings of the Twelth ACM PODS Symposium on Principles of Database Systems, 1993.

....for infinite data and to develop technical tools for studying the data models and query languages. There have been only very few theoretical results on infinite databases. General results on the completeness of query languages for infinite recursive databases were reported by Hirst and Harel in [HH93], where two classes of recursive databases are considered, and it is shown that: i) quantifier free first order logic is complete on the class of all recursive databases, and (ii) a version of Chandra and Harel s QL [CH80] is complete on highly symmetric databases. The first result of [HH93] ....

....in [HH93] where two classes of recursive databases are considered, and it is shown that: i) quantifier free first order logic is complete on the class of all recursive databases, and (ii) a version of Chandra and Harel s QL [CH80] is complete on highly symmetric databases. The first result of [HH93] indicates that the class of recursive structures is much to general for database purposes, since quantifier free first order logic is already complete on this class. Therefore, many basic queries are simply not computable (projection, connectivity, etc. These results reveal the important ....

T. Hirst and D. Harel. Completeness results of recursive data bases. In Proc. 12th ACM Symp. on Principles of Database Systems, pages 244--252, 1993.

....universal domain, has been introduced: a function Q is called C generic if its result is invariant on any permutation OE for which OE(c) c for all c 2 C. Obviously oe A=c is fcg generic. In the case of databases that are not finite but recursive the concept of genericity has been studied in [26]. For spatial databases, however, the definition of genericity depends on the particular kind of geometry in which the spatial information is to be interpreted [34] This interpretation is determined by the spatial database application and the type of queries that are considered to be of ....

T. Hirst and D. Harel. Completeness results for recursive data bases. In Proc. 12th Symp. on Princ. of Database Systems, pages 244--252, 1993.

.... model theory and effective algebra) or in computer science (the constraint programming paradigm) Recursive structures (i.e. relational structures over a countable domain, say the set of nonnegative integers, where every relation is a recursive set of tuples) have been presented by Hirst and Harel [HH93] as a good alternative to finite structures. They have come up with an important trade off between the class of structures taken as semantics and the class of admissible queries, which poses the challenging problem of exhibiting interesting classes that lie between the recursive and the highly ....

.... can be decided in polynomial time in the finite case) becomes Pi 0 3 complete, thus undecidable [Bea76] while Hamiltonicity (a well known NP complete problem for finite graphs) becomes Sigma 1 1 complete, thus even not in the arithmetical hierarchy [Har91] More recently, Hirst and Harel [HH93] studied the recursive structures from a database point of view. Some of their results are worth mentioning. It is known that very primitive relational operators, e.g. projections, do not preserve the recursiveness of relations: if T (x; y; z) ae 3 is the primitive recursive relation ....

T. Hirst and D. Harel. Completeness results for recursive data bases. In Proc. 12th ACM Symp. on Principles of Database Systems, pages 244--252, 1993.

....for infinite data and to develop technical tools for studying the data models and query languages. There has been little investigation on infinite databases in the past. General results on the completeness of query languages for infinite recursive databases were reported by Hirst and Harel in [HH93], where two classes of recursive databases are considered, and it is shown that: 1) Quantifier free first order logic is complete on the class of all recursive databases, and (2) a version of Chandra and Harel s QL [CH80] is complete on highly symmetric databases. The first result of [HH93] ....

....in [HH93] where two classes of recursive databases are considered, and it is shown that: 1) Quantifier free first order logic is complete on the class of all recursive databases, and (2) a version of Chandra and Harel s QL [CH80] is complete on highly symmetric databases. The first result of [HH93] indicates that the class of recursive structures is much too general for database purposes, since quantifier free first order logic is already complete for this class. Therefore, many basic queries are simply not computable (projection, graph connectivity, etc. These results reveal the ....

T. Hirst and D. Harel. Completeness results of recursive data bases. In Proc. 12th ACM Symp. on Principles of Database Systems, pages 244--252, 1993.

....which admits a declarative semantics and an efficient bottom up evaluation in closed form [KKR90] There have been very few theoretical results on infinite databases. General results on the completeness of query languages for infinite recursive databases were reported by Hirst and Harel in [HH93], where it is shown in particular that quantifier free first order logic is complete on the class of all recursive databases. In [KKR90, KG94] the data complexity of both the relational calculus and inflationary Datalog with negation is studied. It was shown that over dense order constraint ....

T. Hirst and D. Harel. Completeness results of recursive data bases. In Proc. 12th ACM Symp. on Principles of Database Systems, pages 244--252, 1993.

....The study of infinite recursive structures has a long tradition in mathematical logic, by the work of Malcev, Nerode, Rabin, Vaught and their scientific descendents. Recently there have been some papers on recursive structures that study questions related to finite model theory. Hirst and Harel [31] investigated recursive databases, given by a finite set of recursive relations over the natural numbers. They studied the notion of a computable query in this context and exhibited complete languages for two specific classes of recursive databases. On the class of all recursive databases, ....

....databases some restrictions on the admissible relations have to be imposed. A natural restriction is that mixed relations be finite and that mixed functions map all but finitely many elements to 0. But there are other possibilities of finite presentations, e.g. that the relations are recursive [31] or given by semi algebraic constraints [42, 26] We won t consider metafinite structures with mixed relations in this paper. However, the design and investigation of query languages for metafinite databases of this kind is one of the promising directions for future research. Another variation, ....

T. Hirst and D. Harel, Completeness Results for Recursive Databases, Journal of Computer and System Sciences, to appear. (Also: 12th ACM Symp. on Principles of Database Systems (1993), 244--252.)

....external functions are of type 2, in that they take as inputs scalar functions. Our emphasis however is on data independence , an issue that is not present in the theory of higher type computability, since the object of discourse there (the natural numbers) are fully interpreted. Hirst and Harel [HH93] consider recursive databases, i.e. databases over a countable domain in which each relation, considered as a set of tuples, is recursive. We could view each external function of a database as infinite binary relations, by considering its graph. Still, our notions of externalfunction domain ....

....considered as a set of tuples, is recursive. We could view each external function of a database as infinite binary relations, by considering its graph. Still, our notions of externalfunction domain independence and computability are totally different from those of genericity and computability of [HH93]. The first reason is because the graphs of recursive functions are in general not recursive, but recursively enumerable [HR87] Even if we restrict the external functions of a database to having recursive graphs, there is a deeper reason for which their framework differs from ours. Namely, Hirst ....

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Tirza Hirst and David Harel. Completeness results for recursive data bases. In Proceedings of 12th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, pages 244--252, Washington, DC, May 1993.

....and (v) zero one laws for recursive structures. 1 Introduction This paper provides a summary of work most of it joint with T. Hirst on infinite recursive (i.e. computable) structures and data bases, and attempts to put it in perspective. The work itself is contained in four papers [H, HH1, HH2, HH3], which are summarized, respectively, in Sections 2, 3, 4 and 5. When computer scientists become interested in an infinite object, they require it to be computable, i.e. recursive, so that it possesses an effective finite representation. Given the prominence of finite graphs in computer science, ....

....versions, particularly the class Sigma 1 1 . Taken together, the two results yield many new problems whose infinite versions are highly undecidable and whose finite versions are outside Max NP. Examples include Max Clique, Max Independent Set, Max Subgraph, and Max Tiling. The next paper, [HH2], summarized in Section 4, puts forward the idea of infinite recursive relational data bases. Such a data base can be defined simply as a finite tuple of recursive relations (not necessarily binary) over some countable domain. We thus obtain a natural generalization of the notion of a finite ....

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T. Hirst and D. Harel, "Completeness Results for Recursive Data Bases", J. Comput. Syst. Sci., to appear. (Also, 12th ACM Symp. on Principles of Database Systems, ACM Press, New York, 1993, 244--252.)

....recursive structures, with recursive graphs as a special case, have been studied quite extensively in the past. Most interesting properties of recursive graphs have been shown to be undecidable, and many are actually outside the arithmetic hierarchy; see, e.g. AMS, Be1, Be2, BG, H, HH1] In [HH2] we considered recursive structures to be generalizations of finite relational data bases, and investigated the class of computable queries over them, the motivation being borrowed from [CH1] A computable query is a (partial) recursive function that is also generic, i.e. it preserves ....

....structures to be generalizations of finite relational data bases, and investigated the class of computable queries over them, the motivation being borrowed from [CH1] A computable query is a (partial) recursive function that is also generic, i.e. it preserves isomorphisms. One of the results of [HH2] is that quantifier free first order logic is complete for recursive data bases, meaning that it expresses precisely the recursive generic queries. Part 1 of this paper deals with languages that can express non recursive queries. If we return for a moment to the world of finite structures, ....

[Article contains additional citation context not shown here]

T. Hirst and D. Harel, "Completeness Results for Recursive Databases", Journal of Computer and System Sciences, to appear. (Also, 12th ACM Symp. on Principles of Database Systems, ACM Press, New York, 1993, pp. 244--252.)

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T. Hirst and D. Harel, Completeness Results for Recursive Databases, Journal of Computer and System Sciences, to appear. (Also: 12th ACM Symp. on Principles of Database Systems (1993), 244--252.)

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