The role of the RM-ODP computational viewpoint concepts in the MDA approach

An MDA design approach should be able to accommodate designs at different levels of platform-independence. We have proposed a design approach previously (in [2]), which allows these levels to be identified. An important feature of this approach is the notion of abstract platform. An abstract platform is determined by the platform characteristics that are relevant for applications at a certain level of platform-independence, and must be established by considering various design goals. In this paper, we define a framework that makes it possible to use RM-ODP concepts in our MDA design approach. This framework allows a recursive application of the computational viewpoint at different levels of platform-independence. This is obtained by equating the RM-ODP notion of infrastructure to our notion of abstract platform

An algorithm for generating abstract syntax trees

The notion of an abstract syntax is discussed. An algorithm is presented for automatically deriving an abstract syntax directly from a BNF grammar. The implementation of this algorithm and its application to the grammar for Modula are discussed

Tameness and frames revisited

We study the problem of extending an abstract independence notion for types of singletons (what Shelah calls a good frame) to longer types. Working in the framework of tame abstract elementary classes, we show that good frames can always be extended to types of independent sequences. As an application, we show that tameness and a good frame imply Shelah's notion of dimension is well-behaved, complementing previous work of Jarden and Sitton. We also improve a result of the first author on extending a frame to larger models.Comment: 36 page

Exceptional orthogonal polynomials and the Darboux transformation

We adapt the notion of the Darboux transformation to the context of polynomial Sturm-Liouville problems. As an application, we characterize the recently described $X_m$ Laguerre polynomials in terms of an isospectral Darboux transformation. We also show that the shape-invariance of these new polynomial families is a direct consequence of the permutability property of the Darboux-Crum transformation.Comment: corrected abstract, added references, minor correction

Syndeticity and independent substitutions

We associate in a canonical way a substitution to any abstract numeration system built on a regular language. In relationship with the growth order of the letters, we define the notion of two independent substitutions. Our main result is the following. If a sequence $x$ is generated by two independent substitutions, at least one being of exponential growth, then the factors of $x$ appearing infinitely often in $x$ appear with bounded gaps. As an application, we derive an analogue of Cobham's theorem for two independent substitutions (or abstract numeration systems) one with polynomial growth, the other being exponential

Linearization of Hyperbolic Finite-Time Processes

We adapt the notion of processes to introduce an abstract framework for dynamics in finite time, i.e.\ on compact time sets. For linear finite-time processes a notion of hyperbolicity namely exponential monotonicity dichotomy (EMD) is introduced, thereby generalizing and unifying several existing approaches. We present a spectral theory for linear processes in a coherent way, based only on a logarithmic difference quotient, prove robustness of EMD with respect to a suitable (semi-)metric and provide exact perturbation bounds. Furthermore, we give a complete description of the local geometry around hyperbolic trajectories, including a direct and intrinsic proof of finite-time analogues of the local (un)stable manifold theorem and theorem of linearized asymptotic stability. As an application, we discuss our results for ordinary differential equations on a compact time-interval.Comment: 32 page

Abstract Interpretation with Unfoldings

We present and evaluate a technique for computing path-sensitive interference conditions during abstract interpretation of concurrent programs. In lieu of fixed point computation, we use prime event structures to compactly represent causal dependence and interference between sequences of transformers. Our main contribution is an unfolding algorithm that uses a new notion of independence to avoid redundant transformer application, thread-local fixed points to reduce the size of the unfolding, and a novel cutoff criterion based on subsumption to guarantee termination of the analysis. Our experiments show that the abstract unfolding produces an order of magnitude fewer false alarms than a mature abstract interpreter, while being several orders of magnitude faster than solver-based tools that have the same precision.Comment: Extended version of the paper (with the same title and authors) to appear at CAV 201