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Satisfiability of Systems of Equations of Real Analytic Functions is Quasi-decidable
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SYSNO ASEP 0368130 Document Type C - Proceedings Paper (int. conf.) R&D Document Type Conference Paper Title Satisfiability of Systems of Equations of Real Analytic Functions is Quasi-decidable Author(s) Franek, Peter (UIVT-O) RID
Ratschan, Stefan (UIVT-O) SAI, RID, ORCID
Zgliczynski, P. (PL)Source Title Mathematical Foundations of Computer Science 2011. - Berlin : Springer, 2011 / Murlak F. ; Sankowski P. - ISSN 0302-9743 - ISBN 978-3-642-22992-3 Pages s. 315-326 Number of pages 12 s. Action MFCS 2011. International Symposium /36./ Event date 22.08.2011-26.08.2011 VEvent location Warsaw Country PL - Poland Event type WRD Language eng - English Country DE - Germany Keywords decidability ; logical theories ; real numbers Subject RIV IN - Informatics, Computer Science R&D Projects OC10048 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) CEZ AV0Z10300504 - UIVT-O (2005-2011) UT WOS 000310341100030 EID SCOPUS 80052134962 DOI 10.1007/978-3-642-22993-0_30 Annotation 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. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2012
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