G. Kuper and M. Y. Vardi. On the Complexity of Queries in the Logical Data Model. Theoretical Computer Science 116:33--58, 1993.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....the domain consists of only those constants occurring in I, so the answer to a query is always finite. The equivalence of the algebra and the calculus has been shown in [AB88] A similar result for the (in some sense more general) logical data model was shown earlier [KV93b] It is also known [HS91, KV93a] that ALG cv (respectively, CALC cv ) expresses the elementary queries, i.e. the queries that are computable [CH80b] in hyper exponential time (space) with respect to the database size. 2.2 Discussion An essential difference between relational calculus and complex value calculus is that the ....

G. Kuper and M. Y. Vardi. On the Complexity of Queries in the Logical Data Model. Theoretical Computer Science 116:33--58, 1993.

....as of the problem of type reconstruction in the ML type discipline. Much is now known about expressibility, but some interesting problems remain open: 1) Determine the exact expressive power of the various fragments of Core ML. Analogous results exist for higher orders in other languages, see [31, 26, 33]. Some progress on this is reported in [25] involving functional characterizations of other complexity classes, in particular PSPACE and EXPTIME. 2) Study optimal reduction strategies [36] in TLC. 3) Study languages that combine list iterators and set iterators ala [6, 8, 7, 28] One ....

G. Kuper and M. Vardi. On the Complexity of Queries in the Logical Data Model. Theoretical Comput. Sci., 116 (1993), pp. 33--57.

....uses fixed order. Finally, we would like to note that our analysis (except for the ML type inference) is for terms of order 5 or less. Beyond order 5 we believe (although we have not worked out the details here) that it should be possible to combine our basic machinery with the reductions of [28, 22, 30] to express various exponential time and space classes. We close with some open questions in Section 8. 2 2 Programming in the Typed Lambda Calculus 2.1 The Simply Typed Lambda Calculus: TLC and TLC = TLC: The syntax of TLC types is given by the grammar T j t j (T T ) where t ranges ....

....PTIME queries and that type inference is efficient. A number of interesting open problems remain, e.g. 1) Determine the exact expressive power of TLI = i and MLI = i for i = 0 and various versions of equality. 2) Determine the expressive power for TLI 2 , as well as for higher orders, see [28, 22, 30]. 3) Determine functional 9 characterizations of other complexity classes, in particular NP, PHIER and PSPACE, see [18, 23, 38, 5] 4) Study optimal reduction strategies [32] in the TLC. 5) Study languages that combine list iterators and set iterators ala [8, 10, 9, 25, 39] ....

G. Kuper and M. Vardi. On the Complexity of Queries in the Logical Data Model. Theoretical Comput. Sci., 116 (1993), pp. 33--57.

....orders, and (2) understanding the expressive power of constants and equality. In terms of comparison of this paper s contribution with related work in descriptive computational complexity: a) Higher order logic has been used to express various exponential time and space classes, e.g. see [25, 22, 15, 26]. However, the exact characterizations given in this paper are more economical in basic primitives. b) There are similarities between the approaches of [21, 20] and [27] Both approaches add primitives to the TLC to encode P. The principal difference is that TLC = equality and constants ....

G. Kuper and M. Vardi. On the Complexity of Queries in the Logical Data Model. Theoretical Computer Science, 116 (1993), pp. 33--57.

....in intermediate results, and the ability to use the powerset operation to create such structures. In particular, one can exhibit a hierarchy of languages, based on restrictions on the types of intermediate results and show that the calculus can express all elementary time (or space) queries [35, 45]. Exact complexity characterizations are obtained with fixpoint, which is no longer redundant when the level of set nesting is bounded [30] The algebra proposed in the earlier models did not incorporate powerset and could not express this operation. It turns out that when considering mappings ....

G. Kuper and M. Y. Vardi, On the complexity of queries in the logical data model, Theoretical Computer Science, 116, 1993, 33--58.

....power of languages for manipulating bags constitutes a new topic of research. On the other hand, there has been a wide interest in languages for hierarchical data structures [KV84, TF86] The complexity and the expressive power of languages for nested relations have been extensively studied [KV88, HS91, PG92, GG92, AFS89, HS89, GV90, GV95]. Collection types have been investigated in [BBN91, BTBW92] in connection with structural recursion. Nested bags, on the other hand had never been addressed. In this paper, we consider algebraic languages for manipulating nested bags, i.e. complex objects constructed by tuple and bag ....

G.M. Kuper and M.Y. Vardi. On the complexity of queries in the logical data model. In Proc. Int. Conf. on Database Theory, pages 267--280, Bruges, 1988.

....complexity which is no more than co NP, hence in PSPACE. This gives an example of a reasonable fragment of the algebra with powerset (namely the image of USO under the embedding) with a PSPACE evaluation strategy, which can express transitive closure. Hull and Su in [HS91] and Kuper and Vardi in [KV93] study the complexity of logics for complex objects. Carried over from logic to the algebra with powerset, their results establish a strict hierarchy of languages corresponding to the depth of nesting of the powerset [HS91] and establish a strong relationship between the expressive power of these ....

....objects. Carried over from logic to the algebra with powerset, their results establish a strict hierarchy of languages corresponding to the depth of nesting of the powerset [HS91] and establish a strong relationship between the expressive power of these languages and certain complexity classes [KV93]. Both results are orthogonal to ours: they concern about what powerset can exrpess, while our result concerns about how efficient powerset can express. Technically, our result is slightly stronger, in that it proves that powerset cannot express efficiently deterministic transitive closure (see ....

Gabriel M. Kuper and Moshe Y. Vardi. On the complexity of queries in the logical data model. Theoretical Computer Science, 116(1):33-- 58, August 1993.

....corresponding to nonrecursive logic programs, see, e.g. 1] Results of this paper show that nonrecursive query languages for complex values are highly intractable. It will be interesting to investigate these classes in terms of fixedparameter complexity similar to the analysis done in [46, 56, 29, 36]. We briefly mention some results on the complexity of recursive logic programs. These (and other results) are surveyed in [18] Definite programs. For definite programs without function symbols, the SUCCESS problem is DEXPTIME complete for recursive programs [55, 30] and PSPACE complete for ....

....of D) and interpret an arbitrary binary relation as a set of pairs fa; bg with elements in D. Analogously, if the atomic domain is finite, but variables and the membership predicate are untyped (polymorphic or interpreted over arbitrary strata) the theory and the problem are also undecidable. [29, 36] investigate the expressive power of database query languages allowing for the powerset constructor, along with explicit boolean connectives and quantifiers 5 . The results of [29, 36] show that the expressive power of such query languages strictly increases as one allows for a deeper nesting of ....

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G. Kuper and M.Y. Vardi. On the complexity of queries in the logical data model. Theoretical Computer Science, 116:33--57, 1993.

....FT83, KV84, SS86] and deductive languages [AG88, BNR 87, Kup87, Kup88] They all use higher order types. Previous investigations of their expressive power have focused on the gain in expressivity resulting from the use of higher order types, when queries are applied to flat databases [HS88, KV88] In this case, the use of higher order types results in very high complexity with respect to the flat input. This paper focuses on queries whose inputs are complex object databases, rather than flat databases. We aim to provide query languages for complex object databases, whose complexity is ....

....existing results, we consider the expressive power of the languages with respect to the queries on flat databases. The fixpoint extensions of the calculi are shown to have precise characterizations in terms of complexity, unlike the previously studied calculi without the fixpoint operators [HS88, KV88] The paper consists of seven sections. In the next section we develop the framework for complex objects, queries and complexity classes of queries on complex objects.This extends the classical framework of Chandra and Harel [CH80] for flat queries. Section 3 reviews calculus based query ....

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G.M. Kuper and M.Y. Vardi. On the complexity of queries in the logical data model. In Proc. Int. Conf. on Database Theory, pages 267--280, Bruges, 1988.

....extension of relational databases, with many practical applications; see [2] for a recent survey. Well known languages in this area are the complex object algebras with or without Powerset of [1] For the analysis of expressibility of the complex object algebra with Powerset we refer to [26, 31] and without Powerset to [39] Note that, although Powerset in [1] is powerful (as are the second order queries in [10, 15, 46] it is an impractical primitive, and much attention has been given to algebras without Powerset for PTIME queries. An elegant way of manipulating complex object ....

....use ALG Gamma . 5.1.3 The Expressive Power of ALG and ALG Gamma A query is an elementary query if it is a computable query and has elementary recursive data complexity 2 with respect to the database size. It turns out that a query is in ALG CALC iff it is an elementary query (we refer to [26, 31] for detailed definitions and proofs) Furthermore, Hull and Su exhibited a hierarchy of classes of queries based on the level of set nesting allowed in temporary predicates [26] One level leads to SO, i.e. relational calculus extended with second order quantification [10] Kuper and Vardi ....

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G. Kuper and M. Vardi. On the Complexity of Queries in the Logical Data Model. Theoretical Comput. Sci., 116 (1993), pp. 33--57.

.... collection type is that of complex objects (see [Hul87, ABGG89, AK89] and the references therein) Variations on the theme are nested relations [JS82] and V relations [SAB 87, AB86] Algebras and or logical calculi (with or without fixpoints) are presented in [KV84, AB88, RKS88, GV91, KV93] as well as in [TF86, SS86, Col90] where they are called nested relational algebras. BBW92] offers a rational reconstruction of the nested relational algebras (NRA) starting from the monad constructs as well as connections between s.r. and the algebra with powerset of [AB88] That NRA at ....

Gabriel M. Kuper and Moshe Y. Vardi. On the complexity of queries in the logical data model. Theoretical Computer Science, 116(1):33--58, August 1993.

....Questions: There are open issues regarding both variations of the input output conventions (see above) and orders above 4. Beyond order 4 we believe (although we have not worked out the details here) that it should be possible to combine our basic machinery with the reductions of [27, 33, 35] to express various exponential time and space classes. Determining the exact expressive power of TLI = i and MLI = i for i 2 is open; the case i = 2 was resolved in [24] and corresponds to PSPACE. With respect to type reconstruction in core ML, the order 3 case is open. For orders of 4 and ....

G. Kuper and M. Vardi. On the Complexity of Queries in the Logical Data Model. Theoretical Comput. Sci., 116 (1993), pp. 33--57.

....an example of a reasonable fragment of the algebra with powerset (namely the image of USO under the embedding) with a PSPACE evaluation strategy, which can express transitive closure. The author was partially supported by grant NSF CCR 90 57570 Hull and Su in [HS91] and Kuper and Vardi in [KV93] study the complexity of logics for complex objects. Carried over from logic to the algebra with powerset, their results establish a strict hierarchy of languages corresponding to the depth of nesting of the powerset [HS91] and establish a strong relationship between the expressive power of these ....

....objects. Carried over from logic to the algebra with powerset, their results establish a strict hierarchy of languages corresponding to the depth of nesting of the powerset [HS91] and establish a strong relationship between the expressive power of these languages and certain complexity classes [KV93]. Both results are orthogonal to ours: they concern about what powerset can express, while our result concerns about how efficiently powerset can express. Technically, our result is slightly stronger, in that it proves that powerset cannot express efficiently deterministic transitive closure ....

Gabriel M. Kuper and Moshe Y. Vardi. On the complexity of queries in the logical data model. Theoretical Computer Science, 116(1):33--58, August 1993.

....that the domain consists of only those constants occurring in I, so the answer to a query is always finite. The equivalence of the algebra and the calculus has been shown in [AB88] A similar result for the (in some sense more general) Logical Data Model was shown earlier [KV93b] It is also known [HS91, KV93a] that ALG cv (respectively, CALC cv ) expresses the elementary queries, i.e. the queries that are computable [CH80b] in hyper exponential time (space) w.r.t. the database size. An essential difference between relational calculus and complex value calculus is that the latter can express ....

G. Kuper and M. Y. Vardi. On the complexity of queries in the logical data model. Theoretical Computer Science 116:33--58, 1993.

....independent query, and hence, by some query evaluated under the limited interpretation. Although invention does not increase the expressive power of the relational calculus, it expands the expressive power of the complex object calculus (from queries having hyperexponential time space complexity [HS91, KV88]) to queries computable by Turing machines with recursive oracles [HS89] We now present several straightforward claims which form part of the proof of Theorem 3.1; the more intricate portions of the proof are presented in the next section. Proof of Theorem 3.1, part 1: In this part of the proof ....

G. M. Kuper and M. Y. Vardi. On the complexity of queries in the Logical Data Model. In M. Gyssens, J. Paredaens, and D. van Gucht, editors, ICDT'88 - Proc. 2nd Int. Conf. on Database Theory, volume 326 of Lecture Notes in Computer Science, pages 267--280. Springer-Verlag, 1988.

....as of the problem of type reconstruction in the ML type discipline. Much is now known about expressibility, but some interesting problems remain open. a) Determine the exact expressive power of the various fragments of Core ML. Analogous results exist for higher orders in other languages, see [31, 26, 33]. Some progress on this is reported in [25] involving functional characterizations of other complexity classes, in particular PSPACE and EXPTIME. 2) Study optimal reduction strategies [36] in the TLC. 3) Study languages that combine list iterators and set iterators ala [6, 8, 7, 28] One ....

G. Kuper and M. Vardi. On the Complexity of Queries in the Logical Data Model. Theoretical Comput. Sci., 116 (1993), pp. 33--57.

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G. Kuper and M. Y. Vardi. On the complexity of queries in the logical data model. Theoretical Computer Science, 116:33--58, 1993.

No context found.

Kuper, G.M. and Vardi, M.Y. (1988), On the complexity of queries in the logical data model.

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