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Computing With FirstOrder Logic
, 1995
"... We study two important extensions of firstorder logic (FO) with iteration, the fixpoint and while queries. The main result of the paper concerns the open problem of the relationship between fixpoint and while: they are the same iff ptime = pspace. These and other expressibility results are obtaine ..."
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Cited by 54 (13 self)
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We study two important extensions of firstorder logic (FO) with iteration, the fixpoint and while queries. The main result of the paper concerns the open problem of the relationship between fixpoint and while: they are the same iff ptime = pspace. These and other expressibility results are obtained using a powerful normal form for while which shows that each while computation over an unordered domain can be reduced to a while computation over an ordered domain via a fixpoint query. The fixpoint query computes an equivalence relation on tuples which is a congruence with respect to the rest of the computation. The same technique is used to show that equivalence of tuples and structures with respect to FO formulas with bounded number of variables is definable in fixpoint. Generalizing fixpoint and while, we consider more powerful languages which model arbitrary computation interacting with a database using a finite set of FO queries. Such computation is modeled by a relational machine...
DomainIndependent Queries on Databases with External Functions
 in &quot;LNCS 893: Proceedings of 5th International Conference on Database Theory,&quot; 177190
, 1995
"... We investigate queries in the presence of external functions with arbitrary inputs and outputs (atomic values, sets, nested sets etc). We propose a new notion of domain independence for queries with external functions which, in contrast to previous work, can also be applied to query languages with f ..."
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Cited by 16 (2 self)
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We investigate queries in the presence of external functions with arbitrary inputs and outputs (atomic values, sets, nested sets etc). We propose a new notion of domain independence for queries with external functions which, in contrast to previous work, can also be applied to query languages with fixpoints or other kinds of iterators. Next, we define two new notions of computable queries with external functions, and prove that they are equivalent, under the assumption that the external functions are total. Thus, our definition of computable queries with external functions is robust. Finally, based on the equivalence result, we give examples of complete query languages with external functions. A byproduct of the equivalence result is the fact that Relational Machines are complete for complex objects: it was known that they are not complete over flat relations. 1 Introduction Database functionalities are important both for practical and for theoretical purposes. E.g. the system O 2 of ...
Queries and Algorithms Computable by Polynomial Time Existential Reflective Machines (Extended Abstract)
, 1996
"... We consider two kinds of reflective relational machines: the usual ones, which use first order queries, and existential reflective machines, which use only first order existential queries. We compare these two computation models. We build on already existing results for standard relational machines, ..."
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We consider two kinds of reflective relational machines: the usual ones, which use first order queries, and existential reflective machines, which use only first order existential queries. We compare these two computation models. We build on already existing results for standard relational machines, obtained by Abiteboul, Papadimitriou and Vianu [APV], so we prove only results for existential machines. First we show that for both standard and existential reflective machines the set of polynomial time computable Boolean queries consists precisely of all PSPACE computable queries. The we go farther and compare which classes of algorithms both kinds of machines represent. It appears that, unless PSPACE = PTIME NP ; there are PSPACE queries which cannot be computed by polynomial time existential reflective machines which use only polynomial amount of relational memory, while it is always possible for standard reflective machines. We conclude that existential reflective machines, although...
Redundant Relations in Relational Databases: A Model Theoretic Perspective
"... Abstract: We initiate in this work the study of a sort of redundancy problem revealed by what we call redundant relations. Roughly, we define a redundant relation in a database instance (dbi) as a kary relation R such that there is a firstorder query which evaluated in the reduced dbi, (i.e., the ..."
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Abstract: We initiate in this work the study of a sort of redundancy problem revealed by what we call redundant relations. Roughly, we define a redundant relation in a database instance (dbi) as a kary relation R such that there is a firstorder query which evaluated in the reduced dbi, (i.e., the dbi without the redundant relation R) gives us R. So, given that firstorder types are isomorphism types on finite structures, we can eliminate that relation R as long as the equivalence classes of the relation of equality of the firstorder types for all ktuples in the dbi are not altered. It turns out that in a fixed dbi, the problem of deciding whether a given relation in the dbi is redundant is decidable, though intractable, as well as the problem of deciding whether there is any relation symbol in the schema which is a redundant relation in the given dbi. We then study redundant relations with a restricted notion of equivalence so that the problem becomes tractable.
Database Interrogation Using Conjunctive Queries
"... We consider a scenario where a client communicates with a database server by posing boolean conjunctive queries, or more generally, counts of conjunctive queries. We investigate to what extent features such as quanti cation, negation, or nonequalities are important in such a setting. ..."
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We consider a scenario where a client communicates with a database server by posing boolean conjunctive queries, or more generally, counts of conjunctive queries. We investigate to what extent features such as quanti cation, negation, or nonequalities are important in such a setting.
Fine Hierarchies of Generic Computation
"... . Suppose that you are a user of a commercial relational database, accessible over the Internet, whose owner has decided to copy the price lists of the US telephone companies  first order queries are for free just like local calls, because they are local by the theorem of Gaifman [6]. All recursi ..."
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. Suppose that you are a user of a commercial relational database, accessible over the Internet, whose owner has decided to copy the price lists of the US telephone companies  first order queries are for free just like local calls, because they are local by the theorem of Gaifman [6]. All recursive queries, being potentially nonlocal, are charged, for simplicity let us assume $1.00 for a Boolean query. NonBoolean queries are certainly not allowed, because the user would require all the data to be sent to him by issuing the first order identity query, and then manipulate with it himself, without any pay. These are the rules. Well, what is your strategy, to compute all you want to know about the database, paying as little as possible? And how much will the total price be? We answer this question, showing that the question whether you can get your answer without any costs at all, depends on whether or not the theories of databases in the provided query language are finitely axiomatiz...