Certified Universal Gathering in R2R^2 for Oblivious Mobile Robots

We present a unified formal framework for expressing mobile robots models, protocols, and proofs, and devise a protocol design/proof methodology dedicated to mobile robots that takes advantage of this formal framework. As a case study, we present the first formally certified protocol for oblivious mobile robots evolving in a two-dimensional Euclidean space. In more details, we provide a new algorithm for the problem of universal gathering mobile oblivious robots (that is, starting from any initial configuration that is not bivalent, using any number of robots, the robots reach in a finite number of steps the same position, not known beforehand) without relying on a common orientation nor chirality. We give very strong guaranties on the correctness of our algorithm by proving formally that it is correct, using the COQ proof assistant. This result demonstrates both the effectiveness of the approach to obtain new algorithms that use as few assumptions as necessary, and its manageability since the amount of developed code remains human readable.Comment: arXiv admin note: substantial text overlap with arXiv:1506.0160

A Sound and Complete Axiomatization of Majority-n Logic

Manipulating logic functions via majority operators recently drew the attention of researchers in computer science. For example, circuit optimization based on majority operators enables superior results as compared to traditional logic systems. Also, the Boolean satisfiability problem finds new solving approaches when described in terms of majority decisions. To support computer logic applications based on majority a sound and complete set of axioms is required. Most of the recent advances in majority logic deal only with ternary majority (MAJ- 3) operators because the axiomatization with solely MAJ-3 and complementation operators is well understood. However, it is of interest extending such axiomatization to n-ary majority operators (MAJ-n) from both the theoretical and practical perspective. In this work, we address this issue by introducing a sound and complete axiomatization of MAJ-n logic. Our axiomatization naturally includes existing majority logic systems. Based on this general set of axioms, computer applications can now fully exploit the expressive power of majority logic.Comment: Accepted by the IEEE Transactions on Computer

Boolean decomposition for AIG optimization

Restructuring techniques for And-Inverter Graphs (AIG), such as rewriting and refactoring, are powerful, scalable and fast, achieving highly optimized AIGs after few iterations. However, these techniques are biased by the original AIG structure and limited by single output optimizations. This paper investigates AIG optimization for area, exploring how far Boolean methods can reduce AIG nodes through local optimization.Boolean division is applied for multi-output functions using two-literal divisors and Boolean decomposition is introduced as a method for AIG optimization. Multi-output blocks are extracted from the AIG and optimized, achieving a further AIG node reduction of 7.76% on average for ITC99 and MCNC benchmarks.Peer ReviewedPostprint (author's final draft

A metric to represent the evolution of CAD/analysis models in collaborative design

Computer Aided Design (CAD) and Computer Aided Engineering (CAE) models are often used during product design. Various interactions between the different models must be managed for the designed system to be robust and in accordance with initially defined specifications. Research published to date has for example considered the link between digital mock-up and analysis models. However design/analysis integration must take into consideration the important number of models (digital mock-up and simulation) due to model evolution in time, as well as considering system engineering. To effectively manage modifications made to the system, the dependencies between the different models must be known and the nature of the modification must be characterised to estimate the impact of the modification throughout the dependent models. We propose a technique to describe the nature of a modification which may be used to determine the consequence within other models as well as a way to qualify the modified information. To achieve this, a metric is proposed that allows the qualification and evaluation of data or information, based on the maturity and validity of information and model

Automatic synthesis of analog layout : a survey

A review of recent research in the automatic synthesis of physical geometry for analog integrated circuits is presented. On introduction, an explanation of the difficulties involved in analog layout as opposed to digital layout is covered. Review of the literature then follows. Emphasis is placed on the exposition of general methods for addressing problems specific to analog layout, with the details of specific systems only being given when they surve to illustrate these methods well. The conclusion discusses problems remaining and offers a prediction as to how technology will evolve to solve them. It is argued that although progress has been and will continue to be made in the automation of analog IC layout, due to fundamental differences in the nature of analog IC design as opposed to digital design, it should not be expected that the level of automation of the former will reach that of the latter any time soon