Reachability in Parametric Interval Markov Chains using Constraints

Parametric Interval Markov Chains (pIMCs) are a specification formalism that extend Markov Chains (MCs) and Interval Markov Chains (IMCs) by taking into account imprecision in the transition probability values: transitions in pIMCs are labeled with parametric intervals of probabilities. In this work, we study the difference between pIMCs and other Markov Chain abstractions models and investigate the two usual semantics for IMCs: once-and-for-all and at-every-step. In particular, we prove that both semantics agree on the maximal/minimal reachability probabilities of a given IMC. We then investigate solutions to several parameter synthesis problems in the context of pIMCs -- consistency, qualitative reachability and quantitative reachability -- that rely on constraint encodings. Finally, we propose a prototype implementation of our constraint encodings with promising results

Set-based design of mechanical systems with design robustness integrated

This paper presents a method for parameter design of mechanical products based on a set-based approach. Set-based concurrent engineering emphasises on designing in a multi-stakeholder environment with concurrent involvement of the stakeholders in the design process. It also encourages flexibility in design through communication in terms of ranges instead of fixed point values and subsequent alternative solutions resulting from intersection of these ranges. These alternative solutions can then be refined and selected according to the designers’ preferences and clients’ needs. This paper presents a model and tools for integrated flexible design that take into account the manufacturing variations as well as the design objectives for finding inherently robust solutions using QCSP transformation through interval analysis. In order to demonstrate the approach, an example of design of rigid flange coupling with a variable number of bolts and a choice of bolts from ISO M standard has been resolved and demonstrated

How to take into account general and contextual knowledge for interactive aiding design: Towards the coupling of CSP and CBR approaches

The goal of this paper is to show how it is possible to support design decisions with two different tools relying on two kinds of knowledge: case-based reasoning operating with contextual knowledge embodied in past cases and constraint filtering that operates with general knowledge formalized using constraints. Our goals are, firstly to make an overview of existing works that analyses the various ways to associate these two kinds of aiding tools essentially in a sequential way. Secondly, we propose an approach that allows us to use them simultaneously in order to assist design decisions with these two kinds of knowledge. The paper is organized as follows. In the first section, we define the goal of the paper and recall the background of case-based reasoning and constraint filtering. In the second section, the industrial problem which led us to consider these two kinds of knowledge is presented. In the third section, an overview of the various possibilities of using these two aiding decision tools in a sequential way is drawn up. In the fourth section, we propose an approach that allows us to use both aiding decision tools in a simultaneous and iterative way according to the availability of knowledge. An example dealing with helicopter maintenance illustrates our proposals

Interval model predictive control

6TH INTERNATIONAL WORKSHOP ON ALGORITHMS AND ARCHITECTURES FOR REAL TIME CONTROL (6) (6.2000.PALMA DE MALLORCA. ESPAÑA)Model Predictive Control is one of the most popular control strategy in the process industry. One of the reason for this success can be attributed to the fact that constraints and uncertainties can be handled. There are many techniques based on interval mathematics that are used in a wide range of applications. These interval techniques can mean an important contribution to Model Predictive Control giving algorithms to achieve global optimization and constraint satisfaction

Weak Bases of Boolean Co-Clones

Universal algebra and clone theory have proven to be a useful tool in the study of constraint satisfaction problems since the complexity, up to logspace reductions, is determined by the set of polymorphisms of the constraint language. For classifications where primitive positive definitions are unsuitable, such as size-preserving reductions, weaker closure operations may be necessary. In this article we consider strong partial clones which can be seen as a more fine-grained framework than Post's lattice where each clone splits into an interval of strong partial clones. We investigate these intervals and give simple relational descriptions, weak bases, of the largest elements. The weak bases have a highly regular form and are in many cases easily relatable to the smallest members in the intervals, which suggests that the lattice of strong partial clones is considerably simpler than the full lattice of partial clones