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ACM Transactions on Graphics (TOG)
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ICCAD '93 Proceedings of the 1993 IEEE/ACM international conference on Computer-aided design
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SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
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TPHOLs '01 Proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics
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SAS '96 Proceedings of the Third International Symposium on Static Analysis
Formal analysis of synchronous circuits
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ACSD '05 Proceedings of the Fifth International Conference on Application of Concurrency to System Design
Three-valued logic in bounded model checking
MEMOCODE '05 Proceedings of the 2nd ACM/IEEE International Conference on Formal Methods and Models for Co-Design
Using three-valued logic to specify and verify algorithms of computational geometry
ICFEM'05 Proceedings of the 7th international conference on Formal Methods and Software Engineering
Using three-valued logic to specify and verify algorithms of computational geometry
ICFEM'05 Proceedings of the 7th international conference on Formal Methods and Software Engineering
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Algorithms that process geometric objects become more and more important for many safety-critical embedded systems, e.g. for motion planning or collision detection, where correctness is indispensable. The main challenge to demonstrating correctness is the consistent handling of degenerate cases like collinear line segments. In this paper, we therefore propose the use of an interactive theorem prover to develop dependable geometry algorithms for safety-critical embedded systems. Our solution is based on the use of a three-valued logic to make degenerate cases explicit. Using the theorem prover, we are not only able to prove the correctness of the obtained algorithms, but also to directly derive a software library of provably correct geometry algorithms for safety-critical applications.