207108480
Weakest Specifunctions for BSP
This paper introduces a calculus of weakest specification for supporting reuse of established components in deriving a design (in the sense of formal methods). The weakest specifunction generalizes the notions of weakest pre-specification and weakest parallel environment; but instead of calculating the weakest required component of a target specification, it calculates the weakest specification function whose value refines the target when applied to an established component. In particular it overcomes the restriction of those other calculi to taking merely one required component at a time. The theory of specifunctions is applied to a new weakest-design calculus in the context of BSP. The calculus is based on the par-seq specifunction which involves two required components: it places one established component in parallel with one required component and the result in sequence with another required component to meet a given specification. A calculus is provided for the par-seq specifunction and it is applied to the derivation of a distributed BSP algorithm for greatest common divisor.
15862425
A Fixpoint Theory for Non-monotonic Parallelism
This paper studies parallel recursions. The trace specification language used in this paper incorporates sequentiality, nondeterminism, reactiveness (including infinite traces), conjunctive parallelism and general recursion. The language is the minimum of its kind and thus provides a context in which we can study parallel recursions in general. In order to use Tarski's theorem to determine the fixpoints of recursions, we need to identify a well-founded partial order. A theorem of this paper shows that no appropriate order exists. Tarski's theorem alone is not enough to determine the fixpoints of parallel recursions. Instead of using Tarski's theorem directly, we reason about the fixpoints of terminating and nonterminating behaviours separately. Such reasoning is supported by the laws of a new composition called partition. We propose a fixpoint technique called the partitioned fixpoint, which is the least fixpoint of the nonterminating behaviours after the terminating behaviours reach their greatest fixpoint. The surprising result is that although a recursion may not be monotonic with regard to the lexical order, it must have the partitioned fixpoint, which equals the least lexical-order fixpoint. Since the partitioned fixpoint is well defined in any complete lattice, the results are applicable to various semantic models. Major existing fixpoint techniques simply become special cases of the partitioned fixpoint. For example, an Egli-Milner-monotonic recursion has its least Egli-Milner fixpoint, which can be shown to be the same as the partitioned fixpoint. The new technique is more general than the least Egli-Milner fixpoint in that the partitioned fixpoint can be determined even when a recursion is not Egli-Milner monotonic. Examples of non-monotonic recursions with fair-interleaving parallelism are studied. Their partitioned fixpoints are shown to be consistent with our intuitions.
13475813
Compositional Reasoning for Pointer Structures
This paper studies the compositional definition and behaviour of properties that arise in pointer structures. A pointer structure is represented as a (pointer) graph. A pointer property is a set of pointer structures. A parameterised binary combinator is defined that enables important properties (like acyclicity, canonicity and reachability) to be defined in a compositional manner. The technique of parameterising a combinator derives from the definition of parallel-by-merge in ‘Unifying Theories of Programming'. It is applied here to the study of disjointness combinators that extend the separating conjunction of Separation Logic. A case study is provided to demonstrate how these ideas are used, in the form of rules of Hoare logic, to verify the correctness of an Object-Oriented program.
8852685
Generic Composition
Abstract. This paper presents a technique called generic composition to provide a uniform basis for modal operators, sequential composition, different kinds of parallel compositions and various healthiness conditions appearing in a variety of semantic theories. The weak inverse of generic composition is defined. A completeness theorem shows that any predicate can be written in terms of generic composition and its weak inverse. A number of algebraic laws that support reasoning are derived.
1010133
A fixpoint theory for non-monotonic parallelism
This paper studies parallel recursion. The trace specification language used in this paper incorporates sequentiality, nondeterminism, reactiveness (including infinite traces), three forms of parallelism (including conjunctive, fair-interleaving and synchronous parallelism) and general recursion. In order to use Tarski’s theorem to determine the fixpoints of recursions, we need to identify a well-founded partial order. Several orders are considered, including a new order called the lexical order, which tends to simulate the execution of a recursion in a similar manner as the Egli-Milner order. A theorem of this paper shows that no appropriate order exists for the language. Tarski’s theorem alone is not enough to determine the fixpoints of parallel recursions. Instead of using Tarski’s theorem directly, we reason about the fixpoints of terminating and nonterminating behaviours separately. Such reasoning is supported by the laws of a new composition called partition. We propose a fixpoint technique called the partitioned fixpoint, which is the least fixpoint of the nonterminating behaviours after the terminating behaviours reach their greatest fixpoint. The surprising result is that although a recursion may not be lexical-order monotonic, it must have the partitioned fixpoint, which is equal to the least lexicalorder fixpoint. Since the partitioned fixpoint is well defined in any complete lattice, the results are applicable to various semantic models. Existing fixpoint techniques simply become special cases of the partitioned fixpoint. For example, an Egli-Milnermonotonic recursion has its least Egli-Milner fixpoint, which can be shown to be the same as the partitioned fixpoint. The new technique is more general than the least Egli-Milner fixpoint in that the partitioned fixpoint can be determined even when a recursion is not Egli-Milner monotonic. Examples of non-monotonic recursions are studied. Their partitioned fixpoints are shown to be consistent with our intuition.
17662809
Hierarchical Organisation of Predicate-Semantic Models
This paper introduces techniques to organise predicate- semantic models in a hierarchical structure so that a new model can inherit the laws of the existing ones. Generic composition is used to simplify the manipulation of predicates. Necessary restrictions are imposed on the definition of each model so that the inheritance relation can be established by checking a few conditions on the healthiness conditions and the commands. Much of the checking can be supported by laws of generic composition. The techniques also help simplify the proof of well-definedness of program combinators (i.e. their closure in the semantic space) so that we no longer need to prove it (in predicate calculus) for every new model.
25374947
A graph-theoretic model for optimizing queries involving methods
Abstract. Traditional algorithms for optimizing the execution order of joins are no more valid when selections and projections involve methods and become very expensive operations. Selections and projections could be even more costly than joins such that they are pulled above joins, rather than pushed down in a query tree. In this paper, we take a fundamental look at how to approach query optimization from a top-down design perspective, rather than trying to force one model to fit into another. We present a graph model which is designed to characterize execution plans. Each edge and each vertex of the graph is assigned a weight to model execution plans. We also design algorithms that use these weights to optimize the execution order of operations. A cost model of these algorithms is developed. Experiments are conducted on the basis of this cost model. The results show that our algorithms are superior to similar work proposed in the literature.
34404148
Stochastic sketching: a new method for global optimization
Abstract In this paper, we propose Stochastic sketching for global optimization based on a simulation of human behaviour. Stochastic sketching tries to do things simply in the human way without too much interpretation instead of modeling the thought and strategies of human beings and applying an artificial model to problems. We introduce and discuss concepts and components essential to stochastic sketching in detail, including sampling guide, zooming controller, sketching model, precision threshold, and satisfaction probability. Experimental results of stochastic sketching on several test functions and a set of recommended parameter settings are given, as well as preliminary comparisons between stochastic sketching and related evolutionary algorithms including evolution strategies, evolutionary programming, and genetic algorithms.
9049589
A service-oriented modeling and simulation framework for rapid development of distributed applications
Abstract The paper presents a service-oriented distributed modeling and simulation framework that supports the development and evaluation of large scale distributed systems such as network-centric and system-of-systems applications. The distinct features of the framework include a modeling and specification language, dynamic model checking for completeness and consistency, automated code generation from the specification, simulation of different architectures with a template-based platform builder, service-oriented multi-agent simulation for easy re-configuration and re-composition, formal policy specification and enforcement for dynamic verification, and dynamic analyses for evaluation and monitoring. The framework and most of the tools reported in this paper have been implemented and applied in several industrial projects. This paper presents the design principles, user interfaces, its runtime infrastructure, and the experiment results on its performance.
28100130
Global Software Enterprise: A New Software Constructing Architecture
Based on current service-oriented architecture (SOA), this paper introduces a consumer-oriented SOA software constructing architecture: the global software enterprise (GSE) architecture. In this architecture, the software construction starts from the consumers' publishing their requirements in the form of application or service specification which they exactly want. The consumer also publishes the expectation for the services the application needs in the form of collaboration specification and test scripts. The service providers then produce services that meet the needs of the applications. This new approach reduces the workload for the consumer and the communication between the consumer and provider. It also extends the design and code sharing, and thus further improves the software productivity
14235163
Robust controllability of interval fractional order linear time invariant systems
We consider uncertain fractional-order linear time invariant (FO-LTI) systems with interval coefficients. Our focus is on the robust controllability issue for interval FO-LTI systems in state-space form. We revisit the controllability problem for the case when there is no interval uncertainty. It turns out that the controllability check for FO-LTI systems amounts to checking the controllability of conventional integer order state space. Based on this fact, we further show that, for interval FO-LTI systems, the key is to check the linear dependency of a set of interval vectors. Illustrative examples are presented.