Complexity of computing topological degree of Lipschitz functions in n dimensions
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Computable analysis: an introduction
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Quantified constraints under perturbation
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CSL '99 Proceedings of the 13th International Workshop and 8th Annual Conference of the EACSL on Computer Science Logic
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SIAM Journal on Numerical Analysis
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ACM Transactions on Computational Logic (TOCL)
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Electronic Notes in Theoretical Computer Science (ENTCS)
Safety verification of non-linear hybrid systems is quasi-semidecidable
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Computing all maps into a sphere
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Delta-Decidability over the Reals
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
CONCUR'12 Proceedings of the 23rd international conference on Concurrency Theory
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In this paper we consider the problem of checking whether a system of equations of real analytic functions is satisfiable, that is, whether it has a solution. We prove that there is an algorithm (possibly non-terminating) for this problem such that (1) whenever it terminates, it computes a correct answer, and (2) it always terminates when the input is robust. A system of equations of robust, if its satisfiability does not change under small perturbations. As a basic tool for our algorithm we use the notion of degree from the field of (differential) topology.