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A model for querying semistructured data through the exploitation of regular sub-structures
Much research has been undertaken in order to speed up the processing of semistructured data in general and XML in particular. Many approaches for storage, compression, indexing and querying exist, e.g. [1, 2]. We do not present yet another such algorithm but a unifying model in which these algorithm can be understood. The key idea behind this research is the assumption, that most practical queries are based on a particular pattern of data that can be deduced from the query and which can then be captured using a regular structure amendable to efficient processing techniques
Data Structures in Classical and Quantum Computing
This survey summarizes several results about quantum computing related to
(mostly static) data structures. First, we describe classical data structures
for the set membership and the predecessor search problems: Perfect Hash tables
for set membership by Fredman, Koml\'{o}s and Szemer\'{e}di and a data
structure by Beame and Fich for predecessor search. We also prove results about
their space complexity (how many bits are required) and time complexity (how
many bits have to be read to answer a query). After that, we turn our attention
to classical data structures with quantum access. In the quantum access model,
data is stored in classical bits, but they can be accessed in a quantum way: We
may read several bits in superposition for unit cost. We give proofs for lower
bounds in this setting that show that the classical data structures from the
first section are, in some sense, asymptotically optimal - even in the quantum
model. In fact, these proofs are simpler and give stronger results than
previous proofs for the classical model of computation. The lower bound for set
membership was proved by Radhakrishnan, Sen and Venkatesh and the result for
the predecessor problem by Sen and Venkatesh. Finally, we examine fully quantum
data structures. Instead of encoding the data in classical bits, we now encode
it in qubits. We allow any unitary operation or measurement in order to answer
queries. We describe one data structure by de Wolf for the set membership
problem and also a general framework using fully quantum data structures in
quantum walks by Jeffery, Kothari and Magniez
The size of BDDs and other data structures in temporal logics model checking
Temporal Logic Model Checking is a verification method in which we describe a system, the model, and then we verify whether important properties, expressed in a temporal logic formula, hold in the system. Many Model Checking tools employ BDDs or some other data structure to represent sets of states. It has been empirically observed that the BDDs used in these algorithms may grow exponentially as the model and formula increase in size. We formally prove that no kind of data structure of polynomial size can represent the set of valid initial states for all models and all formulae. This result holds for all data structures where a state can be checked in polynomial time. Therefore, it holds not only for all types of BDDs regardless of variable ordering, but also for more powerful data structures, such as RBCs, MTBDDs, ADDs and SDDs. Thus, the size explosion of BDDs is not a limit of these specific data representation structures, but is unavoidable: every formalism used in the same way would lead to an exponential size blow up
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