4 research outputs found
Tarski's influence on computer science
The influence of Alfred Tarski on computer science was indirect but
significant in a number of directions and was in certain respects fundamental.
Here surveyed is the work of Tarski on the decision procedure for algebra and
geometry, the method of elimination of quantifiers, the semantics of formal
languages, modeltheoretic preservation theorems, and algebraic logic; various
connections of each with computer science are taken up
Similarity and bisimilarity notions appropriate for characterizing indistinguishability in fragments of the calculus of relations
Motivated by applications in databases, this paper considers various
fragments of the calculus of binary relations. The fragments are obtained by
leaving out, or keeping in, some of the standard operators, along with some
derived operators such as set difference, projection, coprojection, and
residuation. For each considered fragment, a characterization is obtained for
when two given binary relational structures are indistinguishable by
expressions in that fragment. The characterizations are based on appropriately
adapted notions of simulation and bisimulation.Comment: 36 pages, Journal of Logic and Computation 201
Structural characterizations of the navigational expressiveness of relation algebras on a tree
Given a document D in the form of an unordered node-labeled tree, we study
the expressiveness on D of various basic fragments of XPath, the core
navigational language on XML documents. Working from the perspective of these
languages as fragments of Tarski's relation algebra, we give characterizations,
in terms of the structure of D, for when a binary relation on its nodes is
definable by an expression in these algebras. Since each pair of nodes in such
a relation represents a unique path in D, our results therefore capture the
sets of paths in D definable in each of the fragments. We refer to this
perspective on language semantics as the "global view." In contrast with this
global view, there is also a "local view" where one is interested in the nodes
to which one can navigate starting from a particular node in the document. In
this view, we characterize when a set of nodes in D can be defined as the
result of applying an expression to a given node of D. All these definability
results, both in the global and the local view, are obtained by using a robust
two-step methodology, which consists of first characterizing when two nodes
cannot be distinguished by an expression in the respective fragments of XPath,
and then bootstrapping these characterizations to the desired results.Comment: 58 Page
Query processing in temporal object-oriented databases
This PhD thesis is concerned with historical data management in the context of objectoriented
databases. An extensible approach has been explored to processing temporal object queries within a uniform query framework. By the uniform framework, we mean
temporal queries can be processed within the existing object-oriented framework that is extended from relational framework, by extending the existing query processing
techniques and strategies developed for OODBs and RDBs.
The unified model of OODBs and RDBs in UmSQL/X has been adopted as a basis for this purpose. A temporal object data model is thereby defined by incorporating a time
dimension into this unified model of OODBs and RDBs to form temporal relational-like cubes but with the addition of aggregation and inheritance hierarchies. A query algebra,
that accesses objects through these associations of aggregation, inheritance and timereference, is then defined as a general query model /language. Due to the extensive
features of our data model and reducibility of the algebra, a layered structure of query processor is presented that provides a uniforrn framework for processing temporal object
queries. Within the uniform framework, query transformation is carried out based on a set of transformation rules identified that includes the known relational and object rules plus those pertaining to the time dimension. To evaluate a temporal query involving a path with timereference, a strategy of decomposition is proposed. That is, evaluation of an enhanced path, which is defined to extend a path with time-reference, is decomposed by initially dividing the path into two sub-paths: one containing the time-stamped class that can be optimized by
making use of the ordering information of temporal data and another an ordinary sub-path (without time-stamped classes) which can be further decomposed and evaluated using
different algorithms. The intermediate results of traversing the two sub-paths are then joined together to create the query output. Algorithms for processing the decomposed query components, i. e., time-related operation algorithms, four join algorithms (nested-loop forward join, sort-merge forward join, nested-loop reverse join and sort-merge reverse join) and their modifications, have been presented with cost analysis and implemented with stream processing techniques using C++. Simulation results are also provided. Both cost analysis and simulation show the effects of time on the query processing algorithms: the join time cost is linearly increased with the expansion in the number of time-epochs (time-dimension in the case of a regular TS). It is also shown that using heuristics that make use of time information can lead to a significant time cost saving. Query processing with incomplete temporal data has also been discussed