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Satisfiability of Systems of Equations of Real Analytic Functions is Quasi-decidable

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    0368130 - UIVT-O 2012 RIV DE eng C - Konferenční příspěvek (zahraniční konf.)
    Franek, Peter - Ratschan, Stefan - Zgliczynski, P.
    Satisfiability of Systems of Equations of Real Analytic Functions is Quasi-decidable.
    Mathematical Foundations of Computer Science 2011. Berlin: Springer, 2011 - (Murlak, F.; Sankowski, P.), s. 315-326. Lecture Notes in Computer Science, 6907. ISBN 978-3-642-22992-3. ISSN 0302-9743.
    [MFCS 2011. International Symposium /36./. Warsaw (PL), 22.08.2011-26.08.2011]
    Grant CEP: GA MŠk OC10048
    Výzkumný záměr: CEZ:AV0Z10300504
    Klíčová slova: decidability * logical theories * real numbers
    Kód oboru RIV: IN - Informatika

    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.
    Trvalý link: http://hdl.handle.net/11104/0202562
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