Process algebra for performance evaluation

This paper surveys the theoretical developments in the field of stochastic process algebras, process algebras where action occurrences may be subject to a delay that is determined by a random variable. A huge class of resource-sharing systems – like large-scale computers, client–server architectures, networks – can accurately be described using such stochastic specification formalisms. The main emphasis of this paper is the treatment of operational semantics, notions of equivalence, and (sound and complete) axiomatisations of these equivalences for different types of Markovian process algebras, where delays are governed by exponential distributions. Starting from a simple actionless algebra for describing time-homogeneous continuous-time Markov chains, we consider the integration of actions and random delays both as a single entity (like in known Markovian process algebras like TIPP, PEPA and EMPA) and as separate entities (like in the timed process algebras timed CSP and TCCS). In total we consider four related calculi and investigate their relationship to existing Markovian process algebras. We also briefly indicate how one can profit from the separation of time and actions when incorporating more general, non-Markovian distributions

On characteristic points and approximate decision algorithms for the minimum Hausdorff distance

We investigate {\em approximate decision algorithms} for determining whether the minimum Hausdorff distance between two points sets (or between two sets of nonintersecting line segments) is at most $\varepsilon$.\def\eg{(\varepsilon/\gamma)} An approximate decision algorithm is a standard decision algorithm that answers {\sc yes} or {\sc no} except when $\varepsilon$ is in an {\em indecision interval} where the algorithm is allowed to answer {\sc don't know}. We present algorithms with indecision interval $[\delta-\gamma,\delta+\gamma]$ where $\delta$ is the minimum Hausdorff distance and $\gamma$ can be chosen by the user. In other words, we can make our algorithm as accurate as desired by choosing an appropriate $\gamma$. For two sets of points (or two sets of nonintersecting lines) with respective cardinalities $m$ and $n$ our approximate decision algorithms run in time O(\eg^2(m+n)\log(mn)) for Hausdorff distance under translation, and in time O(\eg^2mn\log(mn)) for Hausdorff distance under Euclidean motion

Computational Aspects of the Hausdorff Distance in Unbounded Dimension

We study the computational complexity of determining the Hausdorff distance of two polytopes given in halfspace- or vertex-presentation in arbitrary dimension. Subsequently, a matching problem is investigated where a convex body is allowed to be homothetically transformed in order to minimize its Hausdorff distance to another one. For this problem, we characterize optimal solutions, deduce a Helly-type theorem and give polynomial time (approximation) algorithms for polytopes

The Parma Polyhedra Library: Toward a Complete Set of Numerical Abstractions for the Analysis and Verification of Hardware and Software Systems

Since its inception as a student project in 2001, initially just for the handling (as the name implies) of convex polyhedra, the Parma Polyhedra Library has been continuously improved and extended by joining scrupulous research on the theoretical foundations of (possibly non-convex) numerical abstractions to a total adherence to the best available practices in software development. Even though it is still not fully mature and functionally complete, the Parma Polyhedra Library already offers a combination of functionality, reliability, usability and performance that is not matched by similar, freely available libraries. In this paper, we present the main features of the current version of the library, emphasizing those that distinguish it from other similar libraries and those that are important for applications in the field of analysis and verification of hardware and software systems.Comment: 38 pages, 2 figures, 3 listings, 3 table