A.V. Aho and J.D. Ullman, "Universality of Data Retrieval Languages", Proc. of 6th ACM Symposium on Principles of Programming Languages, 1979, 110-117.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....occur in the same program so it is a clear programmer error, not an ADAMS error In our current implementation of for each elem desig in set desig the set denoted by set desig can not be altered. However, changing this limitation as in [AgG89] would effectively yield fixpoint queries [AhU79]. 30 7. Attribute and Map Inverses ADAMS attributes and maps are, by design, single valued. Expressions of the form element desig . attr desig and element desig . map desig denote a single data value or ADAMS element, respectively. But the essence of much database processing is the access ....

A. V. Aho and J. D. Ullman, Universality of Data Retrieval Languages, Proc. 6th ACM ACM Symp. on Prin. of Programming Languages, San Antonio, TX, Jan. 1979, 110-120.

....g. This is used in the return statement of peekcando, which uses curr to identify the tuples that should be inserted into T. The proof that this cannot be simulated by an element of Pwhen relies on (a generalization of) the fact that the relational calculus cannot compute transitive closure [AU79] trans closure(K) denotes the transitive closure of a binary relation K. This programcan be expressed using the language of [ZH90] with rules that satisfy the conditions stated there for orderindependent rule application. 11 In particular, suppose that the function willnotwork in Pwhen ....

A. V. Aho and J. D. Ullman. Universality of data retrieval languages. In Proc. ACM Symp. on Principles of Programming Languages, pages 110--120, 1979.

....Keywords Data complexity, expressive power, lists, trees, term algebras 1. INTRODUCTION It is well known that rst order logic and other nonrecursive query languages over nite structures cannot express many important relations, for example transitive closure, graph connectivity, acyclicity [3, 13, 15]. The standard way to increase their expressive power is to extend rst order logic by various recursion like operators, such as xpoint operators [3, 9, 2, 19, 30] Is it possible to increase the expressive power by using recursive datastructures instead of recursion like operators For example, ....

.... languages over nite structures cannot express many important relations, for example transitive closure, graph connectivity, acyclicity [3, 13, 15] The standard way to increase their expressive power is to extend rst order logic by various recursion like operators, such as xpoint operators [3, 9, 2, 19, 30]. Is it possible to increase the expressive power by using recursive datastructures instead of recursion like operators For example, one could use lists or trees, probably the most natural recursive datastructures. In this paper we show that the use of lists and trees does not increase the ....

A. Aho and J. Ullman. Universality of data retrieval languages. In ACM Symposium on Principles of Programming Languages, pages 110-117, 1979.

....closure of a graph is not expressible in relational algebra or calculus; in particular, expressions similar to those above (which happen to be unions of conjunctive queries) cannot possibly express it. This appears to be a folk result in the database community; while many papers do refer to [2] or some other source on the expressive power of rst order logic, many texts just state that relational algebra, calculus and SQL cannot express recursive queries such as reachability. With this limitation in mind, the SQL3 standard introduced recursion explicitly into the language [7,12] One ....

A. V. Aho and J. D. Ullman. Universality of data retrieval languages. In Principles of Programming Languages 1979, ACM Press, pages 110-120.

....will presume that the readers are familiar with First Order (FO) logic on these structures, and proceed directly to more expressive logics. 1. 1 Least Fixed Point Logic Perhaps the most popular fixed point logic is the First Order (positive) Least Fixed Point (FO pos LFP) logic of [Mo74] and [AhU79]. First, given a relation variable symbol S, a second order formula ( S; is S positive if it has no second order quantifications and if all occurrences of S in are positive, viz. none are within any negated subformulas. And given a tuple S = S 0 ; S 1 ; S , is ....

A. Aho & J. Ullman, Universality of data retrieval languages, Proc. 6th ACM Symp. Principles of Programming Languages (1979), 110-117.

.... first order relational calculus and the relational algebra of Codd [4] see also [15] the conjunctive queries of Chandra and Merlin [9] and the tableau queries of Aho et al. 1] Zloof [25] has suggested augmenting the first order queries with a transitive closure operator, and Aho and Ullman [2] have augmented the relational algebra with a least fixpoint operator. Some fixpoint queries are also obtained by querying in Kowalski s language of logic programs [15, 17, 22] Chandra and Harel [6] defined the general class CQ of all computable queries which, in some sense, is the largest ....

.... clasification of the firstorder queries (and hence also of the relational algebra queries) of Codd [4] We show the strictness of the first order query hierarchy and a correspondence with the polynomial time hierarchy of Stockmeyer [21] The suggestions of Zloof [25] and of Aho and Ullman [2] concerning transitive closure transcend the first order query hierarchy, but are easily seen to be embedded in the full hierarchy, as do those of Kowalski [17] see also [8] The full hierarchy to level o) 2 is then shown to have natural closure properties. The question of strictness of the ....

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A. V. AHO AND J. D. ULLMAN, Universality of data retrieval languages, in "Proceedings, 6th ACM Syrup. on Principles of Programming Languages," San Antonio, Texas, Jan. 1979, pp. 110-117.

....that one of the reasons for this phenomenon is rooted in the choice made by Codd [8] There, one version of this calculus is taken as the canonical query language, and any other language having at least its power of expression is said (in [8] to be complete. It has been shown by Aho and Ullman [4], however, that certain reasonable queries cannot be expressed in first order relational calculus (in particular, the transitive closure of a binary relation cannot be so expressed) This poses the question of whether there is a natural definition of the set of all reasonable queries. One approach ....

....particular, the transitive closure of a binary relation cannot be so expressed) This poses the question of whether there is a natural definition of the set of all reasonable queries. One approach to this is to add various constructs such as transitive closure, fixpoint operators, and iteration [4, 9, 23] to 156 0022 0000 80 050156 23 02.00 0 Copyright 1980 by Academic Press, Inc. All rights of reproduction in any form reserved. query languages and to compare the expressive power of the resulting languages. This approach has the disadvantage that there is no guarantee that one has in fact ....

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A. V. AHO AND J. D. ULLMAN, Universality of data retrieval languages, in "Proceedings, 6th ACM Symp. on Principles of Programming Languages, San-Antinio, Texas, Jan. 1979," pp. 110-117.

....13] for a comprehensive overview. Notice that all syntactic complexity classes can be captured by generic generalized quantifiers [36, 39, 61] In the context of databases, generalized quantifiers have been used as a means for increasing the expressive capability of database query languages. In [1], the transitive closure quantifier was applied ad hoc since connectivity cannot be expressed in Codd s relational calculus. A more systematic treatment is given in [3, 47] where a formalization of subqueries in SQL by generalized quantifiers is presented, and occurrences of generalized ....

A. Aho and J. Ullman. Universality of Data Retrieval Languages. In Proceedings ACM Symposium on Principles of Programming Languages, pages 110--117, 1979.

.... efficient implementation of these two powerful constructs poses some interesting problems [5, 9, 10, 11, t2, 14, 18, 22, 25, 26, 28] For instance, the technique of using the query constants to search the database efficiently (pushing selection) is frequently inapplicable to recurslye predicates [ 1]. Moreover, the issue of safety, which in relational databases is solved by simple syntactic conditions on the query language, here requires a complex analysis on the bindings passed upon unification [23, 29] This paper studies the problem of implementing safely and efficiently recursire Horn ....

....to identify many situations where the counting set computation becomes trivial and can be eliminated. Therefore, the counting method also supplies a good framework for identifying simple cases where recurslye queries with constants can be implemented safely and efficiently by a single fixpoint [1]. Safety of queries A safe query is one that generates only a finite number of answers. Safety for recurslye queries with function symbols is undecidable; thus the best a person can do is to provide sufficient conditions that cover the cases of practical interests. Our domain of interest ....

A.V. Aho and J. Ullman, Universality of data retrieval languages, in: Proc POPL Confi, rence, San Antonio TX (1979) 110-120.

....to identify many situations where the counting set computation becomes trivial and can be eliminated. Therefore, the counting method also supplies a good framework for identifying simple cases where recurslye queries with constants can be implemented safely and efficiently by a single fixpoint [AhUI]. 5. Safety of Queries A safe query is one that generates only a finite number of answers. Safety for recursive queries with function symbols is undecidable; thus the best a person can do is to provide sufficient conditions that cover the cases of practical interests. Our domain of interest ....

Aho A. V. and J. Ullman," Universality of Data Retrieval Languages," Proc. POPL Conference, San Antonio Tx, 1979. IAC] Aiello, L. and Cecchi, "Adding a Closure Operator to the Extended Relational Algebra ...", Rome Univ. Technical Report, 1985.

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A.V. Aho and J.D. Ullman, "Universality of Data Retrieval Languages", Proc. of 6th ACM Symposium on Principles of Programming Languages, 1979, 110-117.

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A. V. Aho and J. D. Ullman. Universality of data retrieval languages. In Proc. POPL, pages 110--120. ACM, 1979.

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A.V. Aho and J.D. Ullman, "Universality of Data Retrieval Languages," Proc. Sixth Ann. ACM Symp. Principles of Programming Languages (POPL 1979.

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A. Aho and J. Ullman. Universality of data retrieval languages. In Proceedings 6th Symposium on Principles of Programming Languages, Texas, January 1979.

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A. Aho and J. Ullman. Universality of data retrieval languages. In Proceedings 6th Symposium on Principles of Programming Languages, Texas, January 1979.

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A. V. Aho and J. D. Ullman. Universality of data retrieval languages. In Proceedings of 6th Symposium on Principles of Programming Languages, Texas, pages 110--120, January 1979.

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A. V. Aho and J. D. Ullman. Universality of data retrieval languages. In Proceedings of 6th Symposium on Principles of Programming Languages, Texas, pages 110--120, January 1979.

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A. V. Aho and J. D. Ullman, Universality of data retrieval languages, Proc. 6th ACM Symp. on Principles of Programming Languages, 1979, pp. 110--117.

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A. V. Aho and J. D. Ullman, Universality of data retrieval languages, Proc. 6th ACM Symp. on Principles of Programming Languages, 1979, pp. 110--117.

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A.V. Aho and J.D. Ullman. Universality of data retrieval languages. In Proc. 6th ACM Symp. on Principles of Programming Languages, pages 110--117, 1979.

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A. V. Aho and J. D. Ullman. Universality of data retrieval languages. In Proc. 6th ACM Symp. on Principles of Programming Languages, pages 110-117, 1979. 29

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A. Aho and J. Ullman. Universality of data retrieval languages. In Proceedings 6th Symposium on Principles of Programming Languages, Texas, pages 110--120, 1979.

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Alfred V. Aho and Jeffrey D. Ullman. Universality of data retrieval languages. In Sixth ACM Symposium on Principles of Programming Languages (POPL79, proceedings), pages 110--117, 1979.

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A.V. Aho, J.D. Ullman, "The Universality of Data Retrieval Languages," Proc. 6th POPL 1979, 110--120.

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A. V. Aho and J. Ullman, "Universality of data retrieval languages, " in Proc. POPL Conf., San Antonio TX, 1979.

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