2,132 research outputs found
Relational Algebra for In-Database Process Mining
The execution logs that are used for process mining in practice are often
obtained by querying an operational database and storing the result in a flat
file. Consequently, the data processing power of the database system cannot be
used anymore for this information, leading to constrained flexibility in the
definition of mining patterns and limited execution performance in mining large
logs. Enabling process mining directly on a database - instead of via
intermediate storage in a flat file - therefore provides additional flexibility
and efficiency. To help facilitate this ideal of in-database process mining,
this paper formally defines a database operator that extracts the 'directly
follows' relation from an operational database. This operator can both be used
to do in-database process mining and to flexibly evaluate process mining
related queries, such as: "which employee most frequently changes the 'amount'
attribute of a case from one task to the next". We define the operator using
the well-known relational algebra that forms the formal underpinning of
relational databases. We formally prove equivalence properties of the operator
that are useful for query optimization and present time-complexity properties
of the operator. By doing so this paper formally defines the necessary
relational algebraic elements of a 'directly follows' operator, which are
required for implementation of such an operator in a DBMS
A comparison between algebraic query languages for flat and nested databases
AbstractRecently, much attention has been paid to query languages for nested relations. In the present paper, we consider the nested algebra and the powerset algebra, and compare them both mutually as well as to the traditional flat algebra. We show that either nest or difference can be removed as a primitive operator in the powerset algebra. While the redundancy of the nest operator might have been expected, the same cannot be said of the difference. Basically, this result shows that the presence of one nonmonotonic operator suffices in the powerset algebra. As an interesting consequence of this result, the nested algebra without the difference remains complete in the sense of Bancilhon and Paredaens. Finally, we show there are both similarities and fundamental differences between the expressiveness of query languages for nested relations and that of their counterparts for flat relations
Protecting unknown two-qubit entangled states by nesting Uhrig's dynamical decoupling sequences
Future quantum technologies rely heavily on good protection of quantum
entanglement against environment-induced decoherence. A recent study showed
that an extension of Uhrig's dynamical decoupling (UDD) sequence can (in
theory) lock an arbitrary but known two-qubit entangled state to the th
order using a sequence of control pulses [Mukhtar et al., Phys. Rev. A 81,
012331 (2010)]. By nesting three layers of explicitly constructed UDD
sequences, here we first consider the protection of unknown two-qubit states as
superposition of two known basis states, without making assumptions of the
system-environment coupling. It is found that the obtained decoherence
suppression can be highly sensitive to the ordering of the three UDD layers and
can be remarkably effective with the correct ordering. The detailed theoretical
results are useful for general understanding of the nature of controlled
quantum dynamics under nested UDD. As an extension of our three-layer UDD, it
is finally pointed out that a completely unknown two-qubit state can be
protected by nesting four layers of UDD sequences. This work indicates that
when UDD is applicable (e.g., when environment has a sharp frequency cut-off
and when control pulses can be taken as instantaneous pulses), dynamical
decoupling using nested UDD sequences is a powerful approach for entanglement
protection.Comment: 11 pages, 3 figures, published versio
A Conserative Property of a Nested Relational Query Language
We proposed in [7] a nested relational calculus and a nested relational algebra based on structural recursion [6,5] and on monads [27,16]. In this report, we describe relative set abstraction as our third nested relational query language. This query language is similar to the well known list comprehension mechanism in functional programming languages such as Haskell [ll], Miranda [24], KRC [23], etc. This language is equivalent to our earlier query languages both in terms of semantics and in terms of equational theories. This strong sense of equivalence allows our three query languages to be freely combined into a nested relational query language that is robust and user-friendly
On the Complexity of Nonrecursive XQuery and Functional Query Languages on Complex Values
This paper studies the complexity of evaluating functional query languages
for complex values such as monad algebra and the recursion-free fragment of
XQuery.
We show that monad algebra with equality restricted to atomic values is
complete for the class TA[2^{O(n)}, O(n)] of problems solvable in linear
exponential time with a linear number of alternations. The monotone fragment of
monad algebra with atomic value equality but without negation is complete for
nondeterministic exponential time. For monad algebra with deep equality, we
establish TA[2^{O(n)}, O(n)] lower and exponential-space upper bounds.
Then we study a fragment of XQuery, Core XQuery, that seems to incorporate
all the features of a query language on complex values that are traditionally
deemed essential. A close connection between monad algebra on lists and Core
XQuery (with ``child'' as the only axis) is exhibited, and it is shown that
these languages are expressively equivalent up to representation issues. We
show that Core XQuery is just as hard as monad algebra w.r.t. combined
complexity, and that it is in TC0 if the query is assumed fixed.Comment: Long version of PODS 2005 pape
Towards Tractable Algebras for Bags
AbstractBags, i.e., sets with duplicates, are often used to implement relations in database systems. In this paper, we study the expressive power of algebras for manipulating bags. The algebra we present is a simple extension of the nested relation algebra. Our aim is to investigate how the use of bags in the language extends its expressive power and increases its complexity. We consider two main issues, namely (i) the impact of the depth of bag nesting on the expressive power and (ii) the complexity and the expressive power induced by the algebraic operations. We show that the bag algebra is more expressive than the nested relation algebra (at all levels of nesting), and that the difference may be subtle. We establish a hierarchy based on the structure of algebra expressions. This hierarchy is shown to be highly related to the properties of the powerset operator
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