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where each L k with k
1 uses variable x k-1 , L 0 is an expression starting at a
Log schema root in V LS and expression e n+1 uses variable x n . If the details of
the from clause are unimportant , we refer to a Log schema element using the
notation select e from L.
Constraints. For Log schema constraints we consider a very general form of
referential constraints called nested referential integrity constraints (NRIs) [21]
extended to support choice types. NRIs capture naturally relational foreign key
constraints.
Definition 5: An association is a query on a VM log schema V LS
select e n+1 from x 0 in L 0 , x 1 in L 1 ……..x n in L n
where e 1 = e 1 1 and e 2 = e 1 2 and . ........ e n = e 1 n
Definition 6: A mapping is a constraint for each A VLs exist A VTs with C, where
A VLs is an association on a virtual machine log source schema V LS and A VTs is an
association on a virtual machine log target schema VT LS and C is a conjunction
of equality conditions relating atomic type expressions over V LS with atomic
expressions over VT LS .
Definition 7: A correspondence is a specification that describes how the value
of an atomic target VM log schema element is generated from the VM Log
source schema. A correspondence can be represented as simple inter-schema
referential constraints. A correspondence from a source element select e VLS from
from L VLS to a target element select e VTLS from from L VTLS is an inter-schema
NRI for each L VLS exist L VTLS with e VLS = e VTLS . Correspondences are implicit
within the mappings (and view definitions) can be easily extracted from them.
Definition 8: A VM Log association A is dominated by association B (noted
as A B ) if there is a renaming function h from the variables of A to the
variables of B such that the from and where clauses of h(A) are subsets,
respectively of the from and where clauses of B.
Domination can naturally extend to mappings as follows. VM log Mapping m 1 :
for each A VLs 1 exist A VTs 1 with C 1 is dominated by mapping m 2 for each
A VLs 2 exist A VTs 2 with C 2 (denoted as m 1 m 2 ) if A VLs 1 A VTs 2 and
for every equality condition e = e 1 in C 1 , h 1 (e) = h 2 (e 1 ) is in C 2 (or implied by
C 2 ) where h 1 (e) = h 2 (e 1 ) are renaming functions from A VLs 1 to A VTs 1 and
from A VLs 2 to A VTs 2 respectively.
There are three (3) ways in which semantic relationships between schema elements
can be encoded. The first is through the structure of the schema. Elements may be
related by their placement in the same record type or more generally through parent
child relationship in nested schemas. An association containing elements that are
related only through the schema structure is referred to as a structural association.
Structural associations correspond to the primary paths used in where it is shown
that they can be computed by one time traversal over this log schema.
Definition 9: A structural VM Log association is an association
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