14,162 research outputs found

    Generating Property-Directed Potential Invariants By Backward Analysis

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    This paper addresses the issue of lemma generation in a k-induction-based formal analysis of transition systems, in the linear real/integer arithmetic fragment. A backward analysis, powered by quantifier elimination, is used to output preimages of the negation of the proof objective, viewed as unauthorized states, or gray states. Two heuristics are proposed to take advantage of this source of information. First, a thorough exploration of the possible partitionings of the gray state space discovers new relations between state variables, representing potential invariants. Second, an inexact exploration regroups and over-approximates disjoint areas of the gray state space, also to discover new relations between state variables. k-induction is used to isolate the invariants and check if they strengthen the proof objective. These heuristics can be used on the first preimage of the backward exploration, and each time a new one is output, refining the information on the gray states. In our context of critical avionics embedded systems, we show that our approach is able to outperform other academic or commercial tools on examples of interest in our application field. The method is introduced and motivated through two main examples, one of which was provided by Rockwell Collins, in a collaborative formal verification framework.Comment: In Proceedings FTSCS 2012, arXiv:1212.657

    Robust Classification for Imprecise Environments

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    In real-world environments it usually is difficult to specify target operating conditions precisely, for example, target misclassification costs. This uncertainty makes building robust classification systems problematic. We show that it is possible to build a hybrid classifier that will perform at least as well as the best available classifier for any target conditions. In some cases, the performance of the hybrid actually can surpass that of the best known classifier. This robust performance extends across a wide variety of comparison frameworks, including the optimization of metrics such as accuracy, expected cost, lift, precision, recall, and workforce utilization. The hybrid also is efficient to build, to store, and to update. The hybrid is based on a method for the comparison of classifier performance that is robust to imprecise class distributions and misclassification costs. The ROC convex hull (ROCCH) method combines techniques from ROC analysis, decision analysis and computational geometry, and adapts them to the particulars of analyzing learned classifiers. The method is efficient and incremental, minimizes the management of classifier performance data, and allows for clear visual comparisons and sensitivity analyses. Finally, we point to empirical evidence that a robust hybrid classifier indeed is needed for many real-world problems.Comment: 24 pages, 12 figures. To be published in Machine Learning Journal. For related papers, see http://www.hpl.hp.com/personal/Tom_Fawcett/ROCCH

    Relative Convex Hull Determination from Convex Hulls in the Plane

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    A new algorithm for the determination of the relative convex hull in the plane of a simple polygon A with respect to another simple polygon B which contains A, is proposed. The relative convex hull is also known as geodesic convex hull, and the problem of its determination in the plane is equivalent to find the shortest curve among all Jordan curves lying in the difference set of B and A and encircling A. Algorithms solving this problem known from Computational Geometry are based on the triangulation or similar decomposition of that difference set. The algorithm presented here does not use such decomposition, but it supposes that A and B are given as ordered sequences of vertices. The algorithm is based on convex hull calculations of A and B and of smaller polygons and polylines, it produces the output list of vertices of the relative convex hull from the sequence of vertices of the convex hull of A.Comment: 15 pages, 4 figures, Conference paper published. We corrected two typing errors in Definition 2: ISI_S has to be defined based on OSO_S, and IEI_E has to be defined based on OEO_E (not just using OO). These errors appeared in the text of the original conference paper, which also contained the pseudocode of an algorithm where ISI_S and IEI_E appeared as correctly define
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