A maximal independent set in a hypergraph is a subset of vertices that is maximal with respect to the property of not containing any edge of thehypergraph. We show that an algorithm proposed by Beame and Luby is in randomized NC for hypergraphs in which the maximum edge size is bounded by a constant. To prove this, we bound the upper tail of sums of dependent random variables defined on the edges of a hypergraph. These bounds may be viewed as extensions of bounds on the tail of the binomial distribution. We derandomize this algorithm to obtain the first sublinear time deterministic algorithm for hypergraphs with edges of size O(l). The algorithm exhibits the following time-processor tradeofi it can be made to run in time O(n' ) with n"fl l') processors for a hypergraph on n vertices, for any c > 2d+l . '"f$"; here d = O(1) denotes the maximum size of an edge in H. In particular, for any constant e >0, we have an algorithm running in time O(n6 ) on a polynomial number of processors, and we have an algorithm running in time (log)0(1) on~O@S '/ 10S 10S ') processors 1 Introduction A hypergraph H = (~E) consists of a finite set V of vertices (or nodes) and a collection E of non-empty subsets of V called edges. The dimension of H is the maximum size of an edge in E. Thus, a graph is a hypergraph of dimension 2. An independent set in H is a subset of V not containing any edge of H. A maximal independent set (mis) in H is an independent set in H that is not properly contained in some other independent set.We shall now discuss some of the results for this problem. As the model of computation we choose the EREW PRAM, in which concurrent reads or concurrent writes of the same memory location are disallowed (for a discussion of the various PRAM models, see [9]).The question of whether there is an iVC algorithm for finding an mis in an arbitrary hypergraph was posed

Abstract. Model transformations are one of the core artifacts of a model-driven engineering approach. The relational logic language Alloy has been used in the past to verify properties of model transformations. In this paper we introduce the concept of functional Alloy modules. In essence a functional Alloy module can be viewed as an Alloy module representing a model transformation. We describe a sublanguage of Alloy called F-Alloy that allows the specification of functional Alloy modules. Transformations expressed in F-Alloy are analysable using the powerful automatic analysis features of Alloy but can also be interpreted efficiently without the use of backtracking.

Abstract. To define the formal semantics of a modeling language, one normally starts from the abstract syntax and then defines the static semantics and dynamic semantics. Having a formal semantics is important for reasoning about the language but also for building tools for the language. In this paper we propose a novel approach for this task based on the Alloy language. With the help of a concrete example language, we contrast this approach with traditional methods based on formal languages, type checking, meta-modeling and operational semantics. Although both Alloy and traditional techniques yield a formal semantics of the language, the Alloy-based approach has two key advantages: a uniform notation, and immediate automatic analyzability using the Alloy analyzer. Together with the simplicity of Alloy, our approach offers the prospect of making formal definitions easier, hopefully paving the way for a wider adoption of formal techniques in the definition of modeling languages.

Abstract. Software systems are becoming larger and more complex. By tackling the modularisation of crosscutting concerns, aspect orientation draws attention to modularity as a means to address the problems of scalability, complexity and evolution in software systems development. Aspect-oriented modelling (AOM) applies aspect-orientation to the construction of models. Most existing AOM approaches are designed without a formal semantics, and use multi-view partial descriptions of behaviour. This paper presents an AOM approach based on the Visual Contract Language (VCL): a visual language for abstract and precise modelling, designed with a formal semantics, and comprising a novel approach to visual behavioural modelling based on design by contract where behavioural descriptions are total. By applying VCL to a large case study of a car-crash crisis management system, the paper demonstrates how modularity of VCL's constructs, at different levels of granularity, help to tackle complexity. In particular, it shows how VCL's package construct and its associated composition mechanisms are key in supporting separation of concerns, coarse-grained problem decomposition and aspect-orientation. The case study's modelling solution has a clear and well-defined modular structure; the backbone of this structure is a collection of packages encapsulating local solutions to concerns.

Abstract. Model-driven software development aims at easing the process of software development by using models as primary artifacts. Although less complex than the real systems they are based on, models tend to be complex nevertheless, thus making the task of comprehending them non-trivial in many cases. In this paper we propose a technique for model comprehension based on decomposing models into sub-models that conform to the same metamodel as the original model. The main contributions of this paper are: a mathematical description of the structure of these sub-models as a lattice, a linear-time algorithm for constructing this decomposition and finally an application of our decomposition technique to model comprehension.