SODA Conference 2018 Conference Paper
Computing Simplicial Representatives of Homotopy Group Elements
- Marek Filakovský
- Peter Franek
- Uli Wagner 0001
- Stephan Zhechev
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Peter Franek
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3 papers
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3SODA Conference 2014 Conference Paper
Robust Satisfiability of Systems of Equations
- Peter Franek
- Marek Krcál
MFCS Conference 2011 Conference Paper
Satisfiability of Systems of Equations of Real Analytic Functions Is Quasi-decidable
- Peter Franek
- Stefan Ratschan
- Piotr Zgliczynski
Abstract 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.