TY - GEN A1 - Meer, Klaus T1 - Complexity aspects of a semi-infinite optimization problem T2 - Optimization : a Journal of Mathematical Programming and Operations Research Y1 - 2008 SN - 1029-4945 SN - 0233-1934 VL - 57 IS - 1 SP - 143 EP - 152 ER - TY - GEN A1 - Meer, Klaus A1 - Rautenbach, Dieter T1 - On the OBDD size for graphs of bounded tree- and clique-width Y1 - 2009 ER - TY - GEN A1 - Meer, Klaus A1 - Ziegler, Martin T1 - An explicit solution to Post's problem over the reals T2 - Journal of Complexity Y1 - 2008 SN - 0885-064x VL - 24 IS - 1 SP - 3 EP - 15 ER - TY - CHAP A1 - Meer, Klaus A1 - Ziegler, Martin ED - Kučera, Luděk T1 - Real Computational Universality: The word problem for a class of groups with infinite presentation T2 - Mathematical foundations of computer science 2007, 32nd international symposium, MFCS 2007, Český Krumlov, Czech Republic, August 26-31, 2007, proceedings Y1 - 2007 SN - 978-3-540-74455-9 SP - 726 EP - 737 PB - Springer CY - Berlin [u.a.] ER - TY - CHAP A1 - Meer, Klaus A1 - Ziegler, Martin ED - Beckmann, Arnold T1 - Uncomputability below the real halting problem T2 - Second Conference on Computability in Europe, CiE 2006, Swansea, UK, June 30 - July 5, 2006, proceedings. Y1 - 2006 SN - 978-3-540-35466-6 SP - 368 EP - 377 PB - Springer CY - Berlin ER - TY - CHAP A1 - Meer, Klaus ED - Beckmann, Arnold T1 - Optimization and approximation problems related to polynominal system solving T2 - Second Conference on Computability in Europe, CiE 2006, Swansea, UK, June 30 - July 5, 2006, proceedings Y1 - 2006 SN - 978-3-540-35466-6 SP - 360 EP - 367 PB - Springer CY - Berlin ER - TY - CHAP A1 - Meer, Klaus T1 - On the approximation of interval functions Y1 - 2006 ER - TY - CHAP A1 - Flarup Hansen, Uffe A1 - Meer, Klaus ED - Jedrzejowicz, Joanna T1 - Two logical hierarchies of optimization problems over the real numbers T2 - Mathematical Foundations of Computer Science 2005, 30th International Symposium, MFCS 2005, Gdansk, Poland, August 29 - September 2, 2005 Y1 - 2005 SN - 978-3-540-29702-5 SP - 459 EP - 470 PB - Springer CY - Berlin ER - TY - CHAP A1 - Meer, Klaus A1 - Ziegler, Martin ED - Liskiewicz, Maciej T1 - An explicit solution to Post's problem over the reals T2 - Fundamentals of computation theory, 15th international symposium, FCT 2005, Lübeck, Germany, August 17 - 20, 2005 Y1 - 2005 SN - 3-540-28193-2 SP - 456 EP - 467 PB - Springer CY - Berlin ER - TY - CHAP A1 - Meer, Klaus ED - Cooper, Stuart Barry T1 - On some relations between approximation and PCPs over the real numbers T2 - New computational paradigms, First Conference on Computability in Europe, CiE 2005, Amsterdam, The Netherlands, June 8 - 12, 2005 Y1 - 2005 SN - 3-540-26179-6 SP - 322 EP - 331 PB - Springer CY - Heidelberg [u.a.] ER - TY - CHAP A1 - Malajovich, Gregorio A1 - Meer, Klaus T1 - Computing Minimal Multi-Homogeneous Bézout Numbers Is Hard Y1 - 2005 ER - TY - CHAP A1 - Meer, Klaus T1 - Transparent long proofs: A first PCP theorem for NP(R) T2 - Extended Abstract in 31st International Colloquium on Automata, Languages and Programming ICALP 2004, Turku Y1 - 2004 SN - 3-540-22849-7 SP - 959 EP - 970 PB - Springer CY - Berlin ER - TY - BOOK A1 - Jongen, Hubertus Theodor A1 - Meer, Klaus A1 - Triesch, Eberhard T1 - Optimization Theory Y1 - 2004 SN - 978-1-402-08098-2 PB - Kluwer CY - Boston ER - TY - GEN A1 - Meer, Klaus T1 - Simulated Annealing versus Metropolis for a TSP instance T2 - Information Processing Letters Y1 - 2007 SN - 0020-0190 VL - 104 IS - 6 SP - 216 EP - 219 ER - TY - GEN A1 - Malajovich, Gregorio A1 - Meer, Klaus T1 - Computing Minimal Multi-Homogeneous Bézout Numbers Is Hard T2 - Theory of Computing Systems Y1 - 2007 SN - 1432-4350 VL - 40 IS - 4 SP - 553 EP - 570 ER - TY - GEN A1 - Meer, Klaus T1 - On some relations between approximation and PCPs over the real numbers T2 - Theory of Computing Systems Y1 - 2007 SN - 1432-4350 VL - 41 IS - 1 SP - 107 EP - 118 ER - TY - GEN A1 - Flarup Hansen, Uffe A1 - Meer, Klaus T1 - Two logical hierarchies of optimization problems over the real numbers T2 - Mathematical Logic Quaterly Y1 - 2006 SN - 0942-5616 VL - 52 IS - 1 SP - 37 EP - 50 ER - TY - GEN A1 - Meer, Klaus T1 - Transparent long proofs: A first PCP Theorem for NP(R) T2 - Foundations of Computational Mathematics Y1 - 2005 SN - 1615-3375 VL - 5 IS - 3 SP - 231 EP - 255 ER - TY - GEN A1 - Meer, Klaus T1 - Probabilistically checkable proofs over the reals T2 - Electronic notes in theoretical computer science : ENTCS Y1 - 2005 SN - 1571-0661 VL - 123 SP - 165 EP - 177 ER - TY - GEN A1 - Meer, Klaus T1 - On a refined analysis of some problems in interval arithmetic using real number complexity theory T2 - Reliable Computing Y1 - 2004 SN - 1385-3139 VL - 10 IS - 3 SP - 209 EP - 225 ER - TY - CHAP A1 - Gori, Marco A1 - Meer, Klaus ED - Cooper, Stuart Barry T1 - Some aspects of a complexity theory for continuous time systems T2 - Extended abstract, Proceedings Computability in Europe, CiE 2007, Siena, Italy, June 18 - 23, 2007 Y1 - 2007 SN - 978-3-540-73000-2 SP - 554 EP - 565 PB - Springer CY - Berlin ER - TY - CHAP A1 - Meer, Klaus A1 - Rautenbach, Dieter ED - Bodlaender, Hans L. T1 - On the OBDD size for graphs of bounded tree- and clique-width T2 - Parameterized and exact computation, Second International Workshop, IWPEC 2006, Zürich, Switzerland, September 13 - 15, 2006 Y1 - 2006 SN - 978-3-540-39098-5 SP - 72 EP - 83 PB - Springer CY - Berlin [u.a.] ER - TY - CHAP A1 - Flarup Hansen, Uffe A1 - Meer, Klaus ED - Calude, Cristian T1 - Approximation classes for real number optimization problems T2 - Extended abstract, 5th International conference on Unconventional Computation, York, UK, September 4-8, 2006 Y1 - 2006 SN - 978-3-540-38593-6 SP - 86 EP - 100 PB - Springer CY - Berlin ER - TY - CHAP A1 - Meer, Klaus ED - Ambos-Spies, Klaus T1 - On Ladner's Result for a Class of Real Machines with Restricted use of Constants T2 - 5th Conference on Computability in Europe, CiE 2009, Heidelberg, Germany, July 19 - 24, 2009 Y1 - 2009 SN - 978-3-642-03072-7 SP - 352 EP - 361 PB - Springer CY - Heidelber [u.a.] ER - TY - GEN A1 - Meer, Klaus T1 - Fragestellungen aus Mathematik und theoretischer Informatik bei der Konstruktion von Getrieben T2 - Forum der Forschung Y1 - 2008 SN - 0947-6989 VL - 12 IS - 21 SP - 145 EP - 150 ER - TY - GEN A1 - Meer, Klaus A1 - Ziegler, Martin T1 - Real Computational Universality: The word problem for a class of groups with infinite presentation Y1 - 2009 ER - TY - CHAP A1 - Koiran, Pascal A1 - Meer, Klaus T1 - On the Expressive Power of CNF Formulas of Bounded Tree- and Clique-Width T2 - Graph-theoretic concepts in computer science, 34th international workshop, WG 2008, Durham, UK, June 30-July 2, 2008 Y1 - 2008 SN - 978-3-540-92247-6 SP - 252 EP - 263 PB - Springer CY - Berlin [u.a.] ER - TY - GEN A1 - Koiran, Pascal A1 - Meer, Klaus A1 - Briquel, Irénée T1 - On the Expressive Power of CNF Formulas of Bounded Tree- and Clique-Width Y1 - 2011 ER - TY - GEN A1 - Meer, Klaus T1 - Treewidth in Algebraic Complexity Y1 - 2010 ER - TY - CHAP A1 - Meer, Klaus T1 - An Extended Tree-Width Notion for Directed Graphs Related to the Computation of Permanents Y1 - 2011 ER - TY - CHAP A1 - Meer, Klaus T1 - Almost transparent short proof for NP? T2 - Extended abstract, Proceedings 18th International Symposium on Fundamentals of Computation Theory FCT 2011, Oslo, 2011 Y1 - 2011 SN - 978-3-642-22952-7 SP - 41 EP - 52 ER - TY - GEN A1 - Meer, Klaus T1 - On Ladnerʼs result for a class of real machines with restricted use of constants T2 - Information and Computation Y1 - 2012 UR - http://www.sciencedirect.com/science/article/pii/S0890540111001507# SN - 0890-5401 VL - 210 SP - 13 EP - 20 ER - TY - CHAP A1 - Meer, Klaus A1 - Baartse, Martijn T1 - The PCP theorem for NP over the reals T2 - 30th Symposium on Theoretical Aspects of Computer Science STACS , Kiel, 2013 Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0030-drops-39262 UR - http://drops.dagstuhl.de/opus/volltexte/2013/3926/ SP - 104 EP - 115 CY - Leibnitz ER - TY - GEN A1 - Meer, Klaus T1 - Some initial thoughts on bounded query computations over the reals T2 - International Journal of Foundations of Computer Science Y1 - 2012 U6 - https://doi.org/10.1142/S0129054112400618 SN - 0129-0541 N1 - Special Issue on 'Frontier between Decidability and Undecidability and Related Problem' VL - 23 IS - 7 SP - 1499 EP - 1510 ER - TY - CHAP A1 - Meer, Klaus T1 - On the complexity of some problems in interval arithmetic T2 - Proceedings, 28th International Symposium on Mathematical Foundations of Computer Science, Bratislava, Slovakia, 2003 Y1 - 2003 SN - 3-540-40671-9 SP - 582 EP - 591 PB - Springer CY - Berlin [u.a.] ER - TY - CHAP A1 - Jongen, Hubertus Theodor A1 - Meer, Klaus ED - Walz, Guido T1 - Das Simplexverfahren T2 - Lexikon der Mathematik, Band 5 Y1 - 2002 SN - 3-8274-0437-1 SP - 27 EP - 30 PB - Spektrum Akademischer Verlag CY - Heidelberg ER - TY - CHAP A1 - Jongen, Hubertus Theodor A1 - Meer, Klaus ED - Walz, Guido T1 - Ellipsoidmethoden T2 - Lexikon der Mathematik, Band 2 Y1 - 2001 SN - 3-8274-0434-7 SP - 37 EP - 38 PB - Spektrum Akademischer Verlag CY - Heidelberg ER - TY - CHAP A1 - Jongen, Hubertus Theodor A1 - Meer, Klaus ED - Walz, Guido T1 - Innere-Punkte Methoden T2 - Lexikon der Mathematik, Band 2 Y1 - 2001 SN - 3-8274-0434-7 SP - 491 EP - 494 PB - Spektrum Akademischer Verlag CY - Heidelberg ER - TY - GEN A1 - Meer, Klaus T1 - An Extended Tree-Width Notion for Directed Graphs Related to the Computation of Permanents T2 - Theory of Computing Systems Y1 - 2014 SN - 1432-4350 VL - 55 IS - 2 SP - 330 EP - 346 ER - TY - CHAP A1 - Lickteig, Thomas A1 - Meer, Klaus A1 - Pardo, Luis Miguel T1 - Real Computation and Complexity, Dagstuhl seminar Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0030-drops-4994 UR - http://drops.dagstuhl.de/opus/volltexte/2006/499/ PB - Internationale Begegnungs- und Forschungszentrum für Informatik CY - Dagstuhl ER - TY - CHAP A1 - Jongen, Hubertus Theodor A1 - Meer, Klaus ED - Walz, Guido T1 - Optimierung T2 - Faszination Mathematik Y1 - 2003 SN - 3-8274-1419-9 SP - 211 EP - 216 PB - Spektrum Akademischer Verlag CY - Heidelberg ER - TY - JOUR A1 - Meer, Klaus T1 - Syropoulos, Apostolos: Hypercomputation. Berlin : Springer, 2008 JF - AMS Mathematical Reviews Y1 - 2009 SN - 0025-5629 IS - 2009j ER - TY - CHAP A1 - Meer, Klaus A1 - Baartse, Martijn ED - Montaña, José Luis ED - Pardo, Luis Miguel T1 - Topics in Real and Complex Number Complexity Theory T2 - Recent Advances in Real Complexity and Computation Y1 - 2013 UR - http://bookstore.ams.org/conm-604?c=1 SN - 978-0-8218-9150-6 U6 - https://doi.org/10.1090/conm/604 SP - 1 EP - 53 PB - American Mathematical Society CY - Providence, RI ER - TY - GEN A1 - Meer, Klaus A1 - Schmitt, Burkhard A1 - Schreiber, Harold T1 - Dimensional Synthesis of Planar Stephenson-Mechanisms for Motion Generation by Circlepoint Search and Homotopy Methods T2 - Mechanism and Machine Theory N2 - The kinematic synthesis of Stephenson mechanisms for motion generation is often based on specifying arbitrary values for certain kinematic dimensions. If no appropriate values are known, an inadequate choice can make it impossible to find a good mechanism. In the present paper a synthesis method is described where kinematic dimensions can be chosen a priori (to meet side conditions, e.g., a limited area for the locations of the fixed pivots), but do not have to be chosen. A circlepoint search in combination with homotopy methods will be applied. Concerning the homotopy methods two approaches – via the Bézout number and the BKK bound – will be compared. Y1 - 2002 UR - http://www.sciencedirect.com/science/article/pii/S0094114X02000162 U6 - https://doi.org/10.1016/S0094-114X(02)00016-2 SN - 0094-114X VL - 37 IS - 7 SP - 717 EP - 737 ER - TY - GEN A1 - Meer, Klaus A1 - Weber, Gerhard Wilhelm T1 - Some aspects of studying an optimization or decision problem in different computational models T2 - European Journal of Operational Research N2 - In this paper we want to discuss some of the features coming up when analyzing a problem in different complexity theoretic frameworks. The focus will be on two problems. The first is related to mathematical optimization. We consider the quadratic programming problem of minimizing a quadratic polynomial on a polyhedron. We discuss how the complexity of this problem might change if we consider real data together with an algebraic model of computation (the Blum–Shub–Smale model) instead of rational inputs together with the Turing machine model. The results obtained will lead us to the second problem; it deals with the intrinsic structure of complexity classes in models over real- or algebraically closed fields. A classical theorem by Ladner for the Turing model is examined in these different frameworks. Both examples serve well for working out in how far different approaches to the same problem might shed light upon each other. In some cases this will lead to quite diverse results with respect to the different models. On the other hand, for some problems the more general approach can also give a unifying idea why results hold true in several frameworks. The paper is of tutorial character in that it collects some results into the above direction obtained previously. KW - Complexity theory Saturation KW - Algebraic models of computation KW - Linear and quadratic programming KW - Structure of complexity classes Y1 - 2002 UR - http://www.sciencedirect.com/science/article/pii/S0377221702002692 U6 - https://doi.org/10.1016/S0377-2217(02)00269-2 SN - 0377-2217 VL - 143 IS - 2 SP - 406 EP - 418 ER - TY - JOUR A1 - Meer, Klaus T1 - Wegener, Ingo: Komplexitätstheorie. Berlin : Springer, 2003 JF - Jahresbericht der Deutschen Mathematiker-Vereinigung Y1 - 2006 SN - 0012-0456 VL - 108 IS - 2 SP - 5 EP - 8 ER - TY - JOUR A1 - Meer, Klaus T1 - Blum, Lenore [u.a.]: Complexity and real computation. Berlin : Springer, 1998 JF - AMS Mathematical Reviews Y1 - 1999 SN - 0025-5629 IS - 99a SP - 509 EP - 600 ER - TY - GEN A1 - Meer, Klaus A1 - Naif, Ameen T1 - Generalized finite automata over real and complex numbers T2 - Theoretical Computer Science N2 - In a recent work, Gandhi, Khoussainov, and Liu [7] introduced and studied a generalized model of finite automata able to work over arbitrary structures. As one relevant area of research for this model the authors identify studying such automata over particular structures such as real and algebraically closed fields. In this paper we start investigations into this direction. We prove several structural results about sets accepted by such automata, and analyze decidability as well as complexity of several classical questions about automata in the new framework. Our results show quite a diverse picture when compared to the well known results for finite automata over finite alphabets. KW - Generalized finite automata KW - Real and complex number computations KW - Decision problems for automata over uncountable structures Y1 - 2015 UR - http://www.sciencedirect.com/science/article/pii/S0304397515003928 U6 - https://doi.org/10.1016/j.tcs.2015.05.001 SN - 0304-3975 VL - Vol. 591 SP - 85 EP - 98 ER - TY - GEN A1 - Meer, Klaus A1 - Baartse, Martijn T1 - The PCP theorem for NP over the reals T2 - Foundations of Computational Mathematics KW - Probabilistically checkable proofs Real and complex number computations PCP theorem Hilbert Nullstellensatz decision problem Y1 - 2015 UR - http://link.springer.com/article/10.1007/s10208-014-9188-x?sa_campaign=email/event/articleAuthor/onlineFirst U6 - https://doi.org/10.1007/s10208-014-9188-x SN - 1615-3375 VL - 15 IS - 3 SP - 651 EP - 680 ER - TY - CHAP A1 - Meer, Klaus A1 - Baartse, Martijn T1 - An algebraic proof of the real number PCP theorem T2 - Mathematical Foundations of Computer Science 2015 40th International Symposium, MFCS 2015, Milan, Italy, August 24-28, 2015, Proceedings, Part II Y1 - 2015 UR - http://www.springer.com/us/book/9783662480533 SN - 978-3-662-48053-3 U6 - https://doi.org/10.1007/978-3-662-48054-0 SP - 50 EP - 61 PB - Springer-Verlag CY - Berlin [u.a.] ER -