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Showing 1 to 4 of 4 for “"cylindrical algebraic decomposition"”.
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Verification of advanced controllers for safety-critical systems
… term substitution and quantifier elimination by cylindrical algebraic decomposition) algorithms. Any control design requirement (such as satisfactory performance, robustness to uncertainties, stability, etc.) that can be expressed in a first order logic formula can be (in principle) verified by …
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Cylindrical Decomposition Under Application-Oriented Paradigms
… Among the so far implemented methods, QE by cylindrical algebraic decomposition (CAD) is the most important complete method. The aim of this thesis is to develop CAD-based algorithms, which can solve more problems in practice and/or provide more interesting information as output. An algorithm …
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Towards justifying computer algebra algorithms in Isabelle/HOL
… using the Isabelle theorem prover to certify the cylindrical algebraic decomposition (CAD) algorithm, which has been widely implemented to solve non-linear problems in various engineering and mathematical fields. Because of the sophistication of this algorithm, people are in doubt of the …
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Upper and Lower Complexity Bounds for Some Problems in Elementary Geometry
… bounds of some problems in the context of semi-algebraic geometry. We present a brief summary of its contents. In Chapter 1 we analyze the algebraic complexity of the linear programming feasibility problem over the reals and prove non-trivial lower bounds for this problem. The linear programming …