Stable manifolds for holomorphic automorphisms

We give a sufficient condition for the abstract basin of attraction of a sequence of holomorphic self-maps of balls in ℂd to be biholomorphic to ℂd. As a consequence, we get a sufficient condition for the stable manifold of a point in a compact hyperbolic invariant subset of a complex manifold to be biholomorphic to a complex Euclidean space. Our result immediately implies previous theorems obtained by Jonsson–Varolin and by Peters; in particular, we prove (without using Oseledec's theory) that the stable manifold of any point where the negative Lyapunov exponents are well-defined is biholomorphic to a complex Euclidean space. Our approach is based on the solution of a linear control problem in spaces of subexponential sequences, and on careful estimates of the norm of the conjugacy operator by a lower triangular matrix on the space of k-homogeneous polynomial endomorphisms of ℂd

An On-the-fly Tableau-based Decision Procedure for PDL-Satisfiability

We present a tableau-based algorithm for deciding satisfiability for propositional dynamic logic (PDL) which builds a finite rooted tree with ancestor loops and passes extra information from children to parents to separate good loops from bad loops during backtracking. It is easy to implement, with potential for parallelisation, because it constructs a pseudo-model ``on the fly'' by exploring each tableau branch independently. But its worst-case behaviour is 2EXPTIME rather than EXPTIME. A prototype implementation in the TWB (http://twb.rsise.anu.edu.au) is available.Comment: 26 pages, longer version of article in Methods for Modalities 2007; improved readability of proof

Strong Dependencies between Software Components

Component-based systems often describe context requirements in terms of explicit inter-component dependencies. Studying large instances of such systems?such as free and open source software (FOSS) distributions?in terms of declared dependencies between packages is appealing. It is however also misleading when the language to express dependencies is as expressive as boolean formulae, which is often the case. In such settings, a more appropriate notion of component dependency exists: strong dependency. This paper introduces such notion as a first step towards modeling semantic, rather then syntactic, inter-component relationships. Furthermore, a notion of component sensitivity is derived from strong dependencies, with ap- plications to quality assurance and to the evaluation of upgrade risks. An empirical study of strong dependencies and sensitivity is presented, in the context of one of the largest, freely available, component-based system

The Software Heritage Graph Dataset: Large-scale Analysis of Public Software Development History

International audienceSoftware Heritage is the largest existing public archive of software source code and accompanying development history. It spans more than five billion unique source code files and one billion unique commits , coming from more than 80 million software projects. These software artifacts were retrieved from major collaborative development platforms (e.g., GitHub, GitLab) and package repositories (e.g., PyPI, Debian, NPM), and stored in a uniform representation linking together source code files, directories, commits, and full snapshots of version control systems (VCS) repositories as observed by Software Heritage during periodic crawls. This dataset is unique in terms of accessibility and scale, and allows to explore a number of research questions on the long tail of public software development, instead of solely focusing on "most starred" repositories as it often happens

Using Preferences to Tame your Package Manager

International audienceDetermining whether some components can be installed on a system is a complex problem: not only it is NP-complete in the worst case, but there can also be exponentially many solutions to it. Ordinary package managers use ad-hoc heuristics to solve this installation problem and choose a particular solution, making extremely difficult to change or sidestep these heuristics when the result is not the one we expect. When software repositories become complex enough, one gets vastly superior results by delegating dependency handling to a specialised solver, and use optimisation functions (or preferences) to control the class of solutions that are found. The opam package manager relies on the CUDF pivot format, which allows OCaml users that have a CUDF-compliant solver on their machine to reap the benefits of preferences-based dependency resolution. Thanks to the solver farm provided by Irill, these benefits are now extended to the OCaml community at large. In this talk we will present the preferences language and explain how to use it