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.
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.
15321284
From Durational Specifications to TLA Designs of Timed Automata
Different temporal logics tend to emphasise different aspects of a hybrid system. In this paper, we study the predicative interpretation of Duration Calculus (DC) and Temporal Logic of Actions (TLA) and the link between them. A notation called generic composition is used to simplify the manipulation of predicates. The modalities of possibility and necessity become generic composition and its inverse of converse respectively. The transformation between different temporal logics is also characterised as such modalities. The formalism provides a framework in which human experience about hybrid system development can be formalised as refinement laws. A high-level durational specification can be decomposed to two durational specifications driven by an automaton. In such a stepwise design process, durational features are reduced while automaton features increase gradually. The application of the technique is demonstrated in the case study of the gas burner problem.
11936833
The weakest specifunction
The weakest specifunction has been introduced to generalise the notions of weakest prespecification and weakest parallel environment. It calculates the weakest specification function whose value refines the target specification when applied to a given component; thus it forms the basis for compositional refinement, an essential ingredient in program derivation. But unlike those previous calculi it is able to deal with several unknown components simultaneously and hence has wider applicability. In this paper we extend the general theory of the weakest specifunction, identifying those spaces in which it behaves miraculously. The par-seq specifunction places an established component in parallel with a required component and the result in sequence with another required component to meet a given specification. We extend the study of the par-seq specifunction in the context of log s, an intermediate-level language for reactive computing in an abstraction of the PRAM and BSP models of computation, and provide a single complete law for its use in program derivation. The resulting calculus is applied to the derivation of a distributed algorithm for dynamic load balancing.
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.
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.
3177556
A parallel architecture for probabilistic relaxation operations on images
Abstract The design of a parallel architecture for executing probabilistic relaxation operations on two dimensional images is addressed. First of all, the concerned relaxation process is divided into three different parallel operations, i.e. systolic, simultaneous, and pipelined. All these parallel operations are mapped onto a linear array architecture that runs smoothly without any bottleneck in the data flows. The proposed architecture and its components are described. An illustrative running of the relaxation process for an image thresholding application on the architecture is described in some details. The hardware implementation and CAD logic simulation are then given. Finally, performance comparison between the proposed architecture and some existing ones is reported.
832740
Constrained genetic algorithms and their applications in nonlinear constrained optimization
The paper presents a problem-independent framework that unifies various mechanisms for solving discrete constrained nonlinear programming (NLP) problems whose functions are not necessarily differentiable and continuous. The framework is based on the first-order necessary and sufficient conditions in the theory of discrete constrained optimization using Lagrange multipliers. It implements the search for discrete-neighborhood saddle points (SP/sub dn/) by performing ascents in the original-variable subspace and descents in the Lagrange-multiplier subspace. Our study on the various mechanisms shows that CSAGA, a combined constrained simulated annealing and genetic algorithm, performs well. Finally, we apply iterative deepening to determine the optimal number of generations in CSAGA.
3447304
Measuring the Dependability of Web Services for Use in e-Science Experiments
This paper introduces a dependability assessment tool (WSsDAT) for Web Services monitoring and testing. It allows users to evaluate dependability of Web Services from the point of view of their clients by collecting metadata representing a number of dependability metrics. This Java-based tool can be deployed in diverse geographical locations to monitor and test the behavior of a selected set of Web Services within preset time intervals. The graphical user interface of the tool provides real-time statistical data describing dependability of the Web Services under monitoring. The tool makes it possible for the users to identify typical patterns of dependability-specific behavior depending on the time of the day, days of the week or the client locations. In addition, WSsDAT can collect and analyze service dependability measurements during long periods of time, as well as obtaining dependability-related information about current service behavior. The paper reports on a successful series of experiments using this tool for investigating the dependability of two BLAST Web Services which are widely used in the bioinformatics domain. The paper shows how the tool can be employed by e-scientists in making informed choices of the distributed services being used in an in silico experiment and thereby improving their overall dependability.
206858542
Degree Sums and Path-Factors in Graphs
Abstract. Let G be a connected graph of order n and suppose that n=∑i=1kni, where ni≥2 are integers. In this paper we give some sufficient conditions in terms of degree sums to ensure that G contains a spanning subgraph consisting of vertex disjoint paths of orders n1,n2,…,nk.
1550167
Verification of arithmetic circuits using binary moment diagrams
Abstract.Binary moment diagrams (BMDs) provide a canonical representation for linear functions similar to the way binary decision diagrams (BDDs) represent Boolean functions. Within the class of linear functions, we can embed arbitrary functions from Boolean variables to real, rational, or integer values. BMDs can thus model the functionality of data path circuits operating over word-level data. Many important functions, including integer multiplication, that cannot be represented efficiently at the bit level with BDDs, have simple representations at the word level with BMDs. Furthermore, BMDs can represent Boolean functions as a special case. We propose a hierarchical approach to verifying arithmetic circuits, where component modules are first shown to implement their word-level specifications. The overall circuit functionality is then verified by composing the component functions and comparing the result to the word-level circuit specification. Multipliers with word sizes of up to 256 bits have been verified by this technique.