S. Abiteboul and V. Vianu, Generic Computation and Its Complexity, Proceedings of 23rd ACM Symposium on Theory of Computing (1991), 209--219. 50  Home/Search   Document Not in Database   Summary   Related Articles   Check

....translate a formula, we follow the above translation steps and at each intermediate result we use a disjunction over all the possibilities. This concludes the proof. 2 A computational model characterizing FO FP C was introduced in [GO93] as a Turing machine with a relational store inspired from [AV91] There are some tight connections between the computation on the Turing tape of the computational device and the expressions manipulating lists in Pom Algj u;t . It is open if the use of general partially ordered types with duplicates further increases the expressiveness of the language. We ....

S. Abiteboul and V. Vianu. Generic computation and its complexity. In Proc. ACM Symp. on Theory of Computing, New Orleans, May 209-219, 1991.

....cardinality, a problem that from a complexity point of view is extremely simple. It is therefore remarkable that a separation of Ptime and Pspace follows even from a separation of IFP and PFP on arbitrary nite structures, not necessarily being ordered. This result is due to Abiteboul and Vianu [AV91b]. See also [Daw93] Theorem. Ptime = Pspace if, and only if, IFP = PFP. There are also xed point logics capturing the complexity classes NP and Exptime, namely non deterministic and alternating non in ationary xed point logic (see [AVV97] For these logics, similar theorems as above have been ....

S. Abiteboul and V. Vianu. Generic computation and its complexity. In Proc. of the 23rd ACM Symp. on the Theory of Computing, 1991.

.... a Theory of Recursive Structures David Harel Dept. of AppliedMathematics and Computer Science The Weizmann Institute of Science, Rehovot, Israel harelwisdom.weizmann.ac.il Abstract. In computer science, one is interested mainly in finite ob jects. Insofar as infinite objects are of interest, they must be computable, i.e. ....

....example, can be viewed as a recursive data base, since we might be interested in the sines or cosines of infinitely many angles. Instead of keeping them all in a table, which is impossible, we keep rules for computing the values from the angles, and vice versa, which is really just to say that we have an effective way of telling whether an edge is present between nodes i and j in an infinite graph, and this is precisely the notion of a recursive graph. In [HH2] we investigate the class of computable queries over recursive data bases, the motivation being borrowed from [CH1] Since the set ....

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S. Abiteboul and V. Vianu, "Generic Computation and Its Complexity", Procl 2$rd Ann. ACM Syrup. on Theory of Computing, pp. 209-219, ACM Press, New York, 1991.

....is sketched in Section 4.1. Theorem 5 allows us to construct an IFP de nable interpretation (re de ning equality) from arbitrary structures to ordered structures, preserving the meaning of formulas of L , which is used to establish the celebrated theorem of Abiteboul and Vianu. Theorem 6 ([3, 4]) IFP = PFP if, and only if, P = PSPACE. Analogous results can be reproduced for many other complexity classes above P. In fact one can de ne a relational measure of complexity, such that two complexity classes above P are equivalent if, and only if, their relational counterparts are [1] In ....

S. Abiteboul and V. Vianu. Generic computation and its complexity. In Proc. 23rd ACM Symposium on the Theory of Computing, 1991.

.... been studied extensively in database theory and have become a standard for comparing and calibrating the expressive power of other database query languages (cf. Cha88] A subsequent turning point in the study of the connections between logic and complexity was the paper by Abiteboul and Vianu [AV91], which established that the problem of separating xpoint logic LFP from partial xpoint logic PFP on the class of all nite structures is equivalent to the separation of PTIME from PSPACE. This result was further extended by Abiteboul, Vardi, and Vianu [AVV92] to results concerning a whole range ....

....each of these xpoint logics gives rise to what is called a relational complexity class on all nite structures; such a class embodies the salient properties of a corresponding complexity class, but it is de ned in a machine independent and order invariant way. The aforementioned results in [AV91,AVV92] exploit the fact that logics with xpoint operators can be viewed as e ective fragments of the in nitary logic 1 with nitely many variables. During the past several years, the study of 1 became a focal point of research in nite model theory. One of the reasons for the interest in L 1 ....

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S. Abiteboul and V. Vianu. Generic computation and its complexity. In Proc. 23rd ACM Symp. on Theory of Computing, pages 209-219, 1991.

....8225 y Currently visiting INRIA Rocquencourt, France facilitated the integration of logic programming techniques in databases. The main motivation has been that common relational database queries are expressible in relational calculus and algebra [17] Datalog : and various fixpoint logics [4, 5, 29, 13, 14]. Most importantly, as shown in [23, 38] every PTIME query can be expressed using Datalog : on ordered structures; and, as shown in [4] it suffices to use Datalog : syntax under a variety of semantics to express various fixpoint logics. In addition, extensions have been proposed to this ....

....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] ....

S. Abiteboul and V. Vianu. Generic Computation and its Complexity. In Proceedings of the 23rd ACM STOC (1991), pp. 209--219.

....the reader is referred to Section 3) The fact that the classes of problems PSPACE EXT and NP EXT can be captured by logics is interesting in its own right. Our logical equivalence result, mentioned in the previous paragraph, should be compared with Abiteboul and Vianu s seminal result, in [1], that P = PSPACE if, and only if, inductive xed point logic has the same expressibility as partial xed point logic (on the class of all nite structures) Again, note that the classes of problems de nable by the sentences of inductive xed point logic and partial xed point logic have zero one ....

....of all those structures of even size. It is also the case that CUB 2 NSPB(1) by Lemma 4, and that CUB is not de nable in bounded variable in nitary logic, by [20] Consequently, NPSB(1) and so NPSA(1) can not be realized as a fragment of bounded variable in nitary logic, unlike the logics in [1, 2, 4] mentioned in the Introduction. 13 4 Partitioned Petri nets In this section, we show that the class of problems NPSB(1) has a complete problem via quanti er free rst order translations with two built in constants. The particular complete problem is somewhat contrived and peculiar in that it ....

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S. Abiteboul and V. Vianu, Generic computation and its complexity, Proceedings of the 23rd Annual ACM Symposium on Theory of Computing , ACM Press (1991) 209-219.

....results concerning fixed point logics, which are Received July 21, 1998. c # 1998, Association for Symbolic Logic 1079 8986 98 0404 0001 6.40 345 346 MARTIN GROHE central in descriptive complexity. Once they had realized this possibility, Kolaitis, Vardi, and others (see, for example, [1, 2, 17, 54, 53, 63]) developed finite variable logics into the technical framework of a central part of finite model theory. Notably, Abiteboul andVianu [2] introduced a machine model reflecting precisely the expressive power of these logics and used it to prove a fundamental result which states that the complexity ....

....346 MARTIN GROHE central in descriptive complexity. Once they had realized this possibility, Kolaitis, Vardi, and others (see, for example, 1, 2, 17, 54, 53, 63] developed finite variable logics into the technical framework of a central part of finite model theory. Notably, Abiteboul andVianu [2] introduced a machine model reflecting precisely the expressive power of these logics and used it to prove a fundamental result which states that the complexity theoretic question of whether PTIME equals PSPACE is equivalent to the purely logical question of whether least fixed point logic has the ....

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S. Abiteboul and V. Vianu, Generic computation and its complexity, Proceedings of the 23rd ACM symposium on theory of computing, 1991, pp. 209--219.

.... functions: GOOD programs are known to be able to compute precisely all construc3 tive generic graph functions [16] Moreover, DMS is a yardstick for the complexity of such generic computations: it was designed to capture precisely the generic complexity classes introduced by Abiteboul and Vianu [3]. Our second main result is a direct proof of the BP completeness of the GGM model. BP completeness is an intrinsic property of the power of generic computation models, originally introduced in the context of query languages for relational databases by Chandra and Harel [8] 1 In the context ....

....as there is a K labeled node in the graph. 4.2 Generic complexity There is often a serious mismatch between the conventional Turing complexity of a computational task and its complexity when performed in a generic computation model. This phenomenon was studied in detail by Abiteboul and Vianu [3] in the context of traditional domain preserving relational queries. They introduced generic, rather than classical Turing machine, complexity classes, based on a generic computation model, called the generic machine (GM) The GM model is an adaptation of the basic Turing machine model to compute ....

S. Abiteboul and V. Vianu. Generic computation and its complexity. In Proceedings 23rd ACM Symposium on Theory of Computing, pages 209--219, 1991. 25

....to domain preserving database queries: a query language is complete if it can express all Turing computable partial functions from databases to databases that are invariant under every permutation of the universe of possible domain values. The latter criterion, nowadays known as genericity (e.g. [4]) ensures that queries can be computed in a way independent of the encoding of the universe of possible domain values. More recently, object oriented database applications motivated researchers to relax domain preservation by allowing the appearance of new objects in the result of a query [2] ....

....counting queries can be expressed efficiently in IQL swap choice, even when the applications of swap choice are only applied to newly created objects. Although all polynomial time counting queries are constructive, most of these nevertheless cannot be expressed efficiently in IQL alone [4]. In this paper we show a much stronger result. We show that IQL counting and IQL swap choice applied to newly created objects only are polynomialtime equivalent, thereby substantiating our earlier claim: the queries expressible in IQL swap choice form the smallest natural class of ....

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S. Abiteboul and V. Vianu. Generic computation and its complexity. In Proc. 23rd ACM Symp. Theory of Computing, 209--219. 1991.

....of TL can already express all deterministic queries, in particular the counting queries. And, RA new loop programs are trivially semideterministic. However, the counting queries are not efficiently expressible in RA new loop. For example, it follows from results in generic complexity [7] that there is no efficient RA new loop program expressing the parity query. 5.2 Counting semi deterministically We still have to specify precisely what is the class of counting queries. A precisely defined extension of fixpoint logic with counting capabilities has been introduced in [12, ....

S. Abiteboul and V. Vianu. Generic computation and its complexity. In Proceedings 23rd ACM Symposium on Theory of Computing, pages 209--218. ACM Press, 1991.

....to run in polynomial space, it is necessary that all equations occurring in the expression are sparse. Interest in fragments of powerful query languages for which the natural evaluation strategy is polynomial space is not new to database theory research. For example, Abiteboul and Vianu [AV91] showed that the parity query is not expressible in the polynomial space fragment of various computationally complete query languages. Closer to our topic is the work of Suciu and Paredaens [SP97] who showed that queries such as transitive closure and parity are not expressible in the ....

S. Abiteboul and V. Vianu. Generic computation and its complexity. In Proceedings 23rd ACM Symposium on the Theory of Computing, pages 209--219, 1991.

....the result of the query is determined. The query language thus obtained is therefore called fixpoint. Actually, on ordered databases 6 , a query is in ptime if and only if it is expressible in fixpoint. It is an open question whether fixpoint is strictly weaker than while, but it is shown in [4] that this question is equivalent to the renowned open problem in computational complexity on the strict containment of ptime in pspace. Similarly to ts while, the language fixpoint on timestamp representations of temporal databases provides a powerful yet computationally tractable temporal query ....

S. Abiteboul and V. Vianu. Generic computation and its complexity. In Proceedings 23rd ACM Symposium on Theory of Computing, pages 209-- 219, 1991.

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S. Abiteboul and V. Vianu, Generic Computation and Its Complexity, Proceedings of 23rd ACM Symposium on Theory of Computing (1991), 209--219. 50

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Abiteboul and Vianu 1991 Serge Abiteboul and Victor Vianu, "Generic Computation and its Complexity", ACM Symposium on Theory of Computing, 1991, 209--219.

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Serge Abiteboul and Victor Vianu, Generic computation and its complexity, Proc. 23rd A.C.M. Symp. on Theory of Computing (1991) 209-- 219.

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S. Abiteboul and V. Vianu, "Generic Computation And Its Complexity," 32nd IEEE Symposium on FOCS (1991), 209-219.

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S. Abiteboul and V. Vianu. Generic computation and its complexity. In Proceedings of 23rd ACM Symposium on the Theory of Computing, 1991.

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S. Abiteboul and V. Vianu, Generic Computation and Its Complexity, Proceedings of 23rd ACM Symposium on Theory of Computing (1991), 209--219. 50

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S. Abiteboul and V. Vianu. Generic computation and its complexity. In Proc. 23rd ACM Symp. on Theory of Computing, pages 209--219, 1991.

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S. Abiteboul and V. Vianu. Generic computation and its complexity. In Proc. 23rd ACM Symp. on Theory of Computing, pages 209-219, 1991.

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S. Abiteboul and V. Vianu. Generic computation and its complexity. In proc. ACM Symp. on Theory of Computing, New Orleans May 1991.

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S. Abiteboul and V. Vianu. Generic computation and its complexity. In Proceedings of 23rd ACM symposium on theory of computing, pages 209--219, 1991.

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Serge Abiteboul and Victor Vianu, Generic computation and its complexity, Proc. 23rd A.C.M. Symp. on Theory of Computing (1991) 209-- 219.

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