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Closed and logical relations for over and underapproximation of powersets
 In SAS
, 2004
"... Abstract. We redevelop and extend Dams’s results on over and underapproximation with higherorder Galois connections: (1) We show how Galois connections are generated from UGLBLLUBclosed binary relations, and we apply them to lower and upper powerset constructions, which are weaker forms of powe ..."
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Abstract. We redevelop and extend Dams’s results on over and underapproximation with higherorder Galois connections: (1) We show how Galois connections are generated from UGLBLLUBclosed binary relations, and we apply them to lower and upper powerset constructions, which are weaker forms of powerdomains appropriate for abstraction studies. (2) We use the powerset types within a family of logical relations, show when the logical relations preserve UGLBLLUBclosure, and show that simulation is a logical relation. We use the logical relations to rebuild Dams’s mostprecise simulations, revealing the inner structure of overand underapproximation. (3) We extract validation and refutation logics from the logical relations, state their resemblance to HennesseyMilner logic and description logic, and obtain easy proofs of soundness and best precision. Almost all Galoisconnectionbased static analyses are overapproximating: For
Observable Modules and Power Domain Constructions
 Semantics of Programming Languages and Model Theory, volume 5 of Algebra, Logic, and Applications
, 1993
"... An Rmodule M is observable iff all its elements can be distinguished by observing them by means of linear morphisms from M to R. We show that free observable Rmodules can be explicitly described as the cores of the final power domains with characteristic semiring R. Then, the general theory is ap ..."
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Cited by 4 (1 self)
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An Rmodule M is observable iff all its elements can be distinguished by observing them by means of linear morphisms from M to R. We show that free observable Rmodules can be explicitly described as the cores of the final power domains with characteristic semiring R. Then, the general theory is applied to the cases of the lower and the upper semiring. All lower modules are observable, whereas there are nonobservable upper modules. Accordingly, all known lower power constructions coincide, whereas there are at least three different upper power constructions. We show that they coincide for continuous ground domains, but differ on more general domains. 1 Introduction A power domain construction maps every domain X into a socalled power domain over X whose points represent sets of points of the ground domain. Power domain constructions were originally proposed to model the semantics of nondeterministic programming languages [Plo76, Smy78, HP79, Mai85]. Other motivations are the sema...
A Query Model to Synthesize Answer Intervals from Indexed Video Units
 IEEE Trans. on Knowledge and Data Eng. Vol.13
, 2001
"... Abstract—While a query result in a traditional database is a subset of the database, in a video database, it is a set of subintervals extracted from the raw video sequence. It is very hard, if not impossible, to predetermine all the queries that will be issued in future, and all the subintervals tha ..."
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Abstract—While a query result in a traditional database is a subset of the database, in a video database, it is a set of subintervals extracted from the raw video sequence. It is very hard, if not impossible, to predetermine all the queries that will be issued in future, and all the subintervals that will become necessary to answer them. As a result, conventional query frameworks are not applicable to video databases. In this paper, we propose a new video query model that computes query results by dynamically synthesizing needed subintervals from fragmentary indexed intervals in the database. We introduce new interval operations required for that computation. We also propose methods to compute relative relevance of synthesized intervals to a given query. A query result is a list of synthesized intervals sorted in the order of their degree of relevance. Index Terms—video database, video retrieval, continuous data, indexing units, interval query, interval operations I.
Algorithms for the Sandbag: An Approach to Imprecise Set Representation
, 1993
"... The sandbag expressively models uncertainty, imprecision, and varying quality of information about a set. This paper describes an approach to constructing sandbags incrementally from a set of constraints called a fact set. The complexities of fundamental sandbag operations using the fact set approac ..."
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The sandbag expressively models uncertainty, imprecision, and varying quality of information about a set. This paper describes an approach to constructing sandbags incrementally from a set of constraints called a fact set. The complexities of fundamental sandbag operations using the fact set approach depend on the application, but are generally intractable. However, by sacrificing optimality, reasonably efficient algorithms can be obtained. This paper describes a data structure and algorithms that produce suboptimal results with polynomial worst case running times in the number of facts. Further, it proves that optimal polynomial algorithms exist for important special cases. It also suggests uses for the sandbag, such as as a general approach to representing sets generated by statistical sampling or as a component of a multimedia DBMS. The goals of this document are to motivate and explain the sandbag, convince the reader that it can be implemented, and to provide sufficiently detailed...
"Your Time is Up": Approximate Query Answering in Deductive Databases
, 1990
"... ions (AGAA90), pages 175185, July 1990, Boston, Massachusetts. Tomasz Imielinski Mukesh Dalal y Rutgers University Department of Computer Science New Brunswick, NJ 08903 Abstract There are two conflicting requirements imposed on modern database systems: high expressive power (leading to high ..."
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ions (AGAA90), pages 175185, July 1990, Boston, Massachusetts. Tomasz Imielinski Mukesh Dalal y Rutgers University Department of Computer Science New Brunswick, NJ 08903 Abstract There are two conflicting requirements imposed on modern database systems: high expressive power (leading to high complexity) and fast response time. We feel that this conflict can be resolved through an appropriate notion of approximate query evaluation. We formulate here foundations of a theory of approximate query answering by providing the notion of justified partial answers. We also introduce cautious query evaluation procedures which always converge to justified partial answers. 1 Introduction One of the major challenges facing the database field is performing complex deductions in the presence of very large amounts of data. This is, in general, a formidable task requiring enormous computational resources. Even processing of a single recursive DATALOG rule, like transitive closure, can be prohib...
Algorithms for Multiresolution Databases
, 1994
"... The use of data at different levels of resolution or multiresolution is a common technique for improving performance of multimedia and scientific database applications, but is not yet systematically supported by database management systems. The sandbag construct, which has been previously suggested ..."
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The use of data at different levels of resolution or multiresolution is a common technique for improving performance of multimedia and scientific database applications, but is not yet systematically supported by database management systems. The sandbag construct, which has been previously suggested as a basis for a data model of multimedia and scientific database, is a generalization of histograms that can model diverse types of data at different levels of resolutions or qualities. A sandbag can hold multimedia data such as motion video and represent incremental improvement in that data. It can be used conveniently to communicate multiresolution information between a standard DBMS and an application by adding a software layer between the DBMS and application. A mechanism for incrementally constructing sandbags of varying descriptiveness from individual facts is presented. A restriction is described that allows sandbags to be efficiently computed. A data structure and algorithms that im...