Abstract: The usual correctness condition for a schedule of
concurrent database transactions is some form of serializability of
the transactions. For general forms, the problem of deciding whether
a schedule is serializable is NP-complete. In those cases other approaches
to proving correctness, using proof rules that allow the steps
of the proof of serializability to be guided manually, are desirable.
Such an approach is possible in the case of conflict serializability
which is proved algebraically by deriving serial schedules using
commutativity of non-conflicting operations. However, conflict serializability
can be an unnecessarily strong form of serializability restricting
concurrency and thereby reducing performance. In practice,
weaker, more general, forms of serializability for extended models of
transactions are used. Currently, there are no known methods using
proof rules for proving those general forms of serializability. In this
paper, we define serializability for an extended model of partitioned
transactions, which we show to be as expressive as serializability
for general partitioned transactions. An algebraic method for proving
general serializability is obtained by giving an initial-algebra specification
of serializable schedules of concurrent transactions in the
model. This demonstrates that it is possible to conduct algebraic
proofs of correctness of concurrent transactions in general cases.
Abstract: In mobile environments, unspecified numbers of transactions
arrive in continuous streams. To prove correctness of their
concurrent execution a method of modelling an infinite number of
transactions is needed. Standard database techniques model fixed
finite schedules of transactions. Lately, techniques based on temporal
logic have been proposed as suitable for modelling infinite schedules.
The drawback of these techniques is that proving the basic
serializability correctness condition is impractical, as encoding (the
absence of) conflict cyclicity within large sets of transactions results
in prohibitively large temporal logic formulae. In this paper, we show
that, under certain common assumptions on the graph structure of
data items accessed by the transactions, conflict cyclicity need only
be checked within all possible pairs of transactions. This results in
formulae of considerably reduced size in any temporal-logic-based
approach to proving serializability, and scales to arbitrary numbers
of transactions.
Abstract: Star graphs are Cayley graphs of symmetric groups of permutations, with transpositions as the generating sets. A star graph is a preferred interconnection network topology to a hypercube for its ability to connect a greater number of nodes with lower degree. However, an attractive property of the hypercube is that it has a Hamiltonian decomposition, i.e. its edges can be partitioned into disjoint Hamiltonian cycles, and therefore a simple routing can be found in the case of an edge failure. The existence of Hamiltonian cycles in Cayley graphs has been known for some time. So far, there are no published results on the much stronger condition of the existence of Hamiltonian decompositions. In this paper, we give a construction of a Hamiltonian decomposition of the star graph 5-star of degree 4, by defining an automorphism for 5-star and a Hamiltonian cycle which is edge-disjoint with its image under the automorphism.
Abstract: We present an operator for a propositional linear temporal logic over infinite schedules of iterated transactions, which, when applied to a formula, asserts that any schedule satisfying the formula is serializable. The resulting logic is suitable for specifying and verifying consistency properties of concurrent transaction management systems, that can be defined in terms of serializability, as well as other general safety and liveness properties. A strict form of serializability is used requiring that, whenever the read and write steps of a transaction occurrence precede the read and write steps of another transaction occurrence in a schedule, the first transaction must precede the second transaction in an equivalent serial schedule. This work improves on previous work in providing a propositional temporal logic with a serializability operator that is of the same PSPACE complete computational complexity as standard propositional linear temporal logic without a serializability operator.
Abstract: Existing work in temporal logic on representing the
execution of infinitely many transactions, uses linear-time temporal
logic (LTL) and only models two-step transactions. In this paper,
we use the comparatively efficient branching-time computational tree
logic CTL and extend the transaction model to a class of multistep
transactions, by introducing distinguished propositional variables
to represent the read and write steps of n multi-step transactions
accessing m data items infinitely many times. We prove that the
well known correspondence between acyclicity of conflict graphs
and serializability for finite schedules, extends to infinite schedules.
Furthermore, in the case of transactions accessing the same set of
data items in (possibly) different orders, serializability corresponds
to the absence of cycles of length two. This result is used to give an
efficient encoding of the serializability condition into CTL.
Abstract: Most of the concurrent transactional protocols consider
serializability as a correctness criterion of the transactions execution.
Usually, the proof of the serializability relies on mathematical proofs
for a fixed finite number of transactions. In this paper, we introduce
a protocol to deal with an infinite number of transactions which are
iterated infinitely often. We specify serializability of the transactions
and the protocol using a specification language based on temporal
logics. It is worthwhile using temporal logics such as LTL (Lineartime
Temporal Logic) to specify transactions, to gain full automatic
verification by using model checkers.