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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 53 (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 "LNCS 893: Proceedings of 5th International Conference on Database Theory," 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 13 (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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Cited by 1 (0 self)
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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...
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.