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  1. ; ; ; ( , 30th International Conference Tools and Algorithms for the Construction and Analysis of Systems)
    Finkbeiner, Bernd ; Kovacs, Laura (Ed.)
    With the growing use of deep neural networks(DNN) in mis- sion and safety-critical applications, there is an increasing interest in DNN verification. Unfortunately, increasingly complex network struc- tures, non-linear behavior, and high-dimensional input spaces combine to make DNN verification computationally challenging. Despite tremen- dous advances, DNN verifiers are still challenged to scale to large ver- ification problems. In this work, we explore how the number of stable neurons under the precondition of a specification gives rise to verifica- tion complexity. We examine prior work on the problem, adapt it, and develop several novel approaches to increase stability. We demonstrate that neuron stability can be increased substantially without compromis- ing model accuracy and this yields a multi-fold improvement in DNN verifier performance. 
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    Free, publicly-accessible full text available April 6, 2025
  2. ; ( , Tools and Algorithms for the Construction and Analysis of Systems (TACAS-24))
    Finkbeiner, Bernd ; Kovács, Laura (Ed.)
    Satisfiability solving has been used to tackle a range of long-standing open math problems in recent years. We add another success by solving a geometry problem that originated a century ago. In the 1930s, Esther Klein’s exploration of unavoidable shapes in planar point sets in general position showed that every set of five points includes four points in convex position. For a long time, it was open if an empty hexagon, i.e., six points in convex position without a point inside, can be avoided. In 2006, Gerken and Nicolás independently proved that the answer is no. We establish the exact bound: Every 30-point set in the plane in general position contains an empty hexagon. Our key contributions include an effective, compact encoding and a search-space partitioning strategy enabling linear-time speedups even when using thousands of cores. 
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    Free, publicly-accessible full text available April 4, 2025