@inbook{Franek2011,
    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.},
    Address = {Berlin, Heidelberg},
    Author = {Franek, Peter and Ratschan, Stefan and Zgliczynski, Piotr},
    BookTitle = {Mathematical Foundations of Computer Science 2011: 36th International Symposium, MFCS 2011, Warsaw, Poland, August 22-26, 2011. Proceedings},
    Editor = {Murlak, Filip and Sankowski, Piotr},
    File = {Satisfiability\_of\_Systems\_of\_Equations\_of\_Real\_Ana (0) - a - a - t.pdf},
    ISBN = {978-3-642-22993-0},
    Pages = {315--326},
    Publisher = {Springer Berlin Heidelberg},
    Title = {Satisfiability of Systems of Equations of Real Analytic Functions Is Quasi-decidable},
    URL = {https://doi.org/10.1007/978-3-642-22993-0\_30},
    Year = {2011},
    bdsk-url-1 = {https://doi.org/10.1007/978-3-642-22993-0\_30},
    bdsk-url-2 = {http://dx.doi.org/10.1007/978-3-642-22993-0\_30},
    date-added = {2017-11-02 09:40:02 +0000},
    date-modified = {2017-11-02 09:40:02 +0000},
    doi = {10.1007/978-3-642-22993-0_30}
}

@inbook{Franek2011, 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.}, Address = {Berlin, Heidelberg}, Author = {Franek, Peter and Ratschan, Stefan and Zgliczynski, Piotr}, BookTitle = {Mathematical Foundations of Computer Science 2011: 36th International Symposium, MFCS 2011, Warsaw, Poland, August 22-26, 2011. Proceedings}, Editor = {Murlak, Filip and Sankowski, Piotr}, File = {Satisfiability_of_Systems_of_Equations_of_Real_Ana (0) - a - a - t.pdf}, ISBN = {978-3-642-22993-0}, Pages = {315--326}, Publisher = {Springer Berlin Heidelberg}, Title = {Satisfiability of Systems of Equations of Real Analytic Functions Is Quasi-decidable}, URL = {https://doi.org/10.1007/978-3-642-22993-0_30}, Year = {2011}, bdsk-url-1 = {https://doi.org/10.1007/978-3-642-22993-0_30}, bdsk-url-2 = {http://dx.doi.org/10.1007/978-3-642-22993-0_30}, date-added = {2017-11-02 09:40:02 +0000}, date-modified = {2017-11-02 09:40:02 +0000}, doi = {10.1007/978-3-642-22993-0_30} }