TY - GEN A1 - Meer, Klaus T1 - On the relations between discrete and continuous complexity theory T2 - Mathematical Logic Quarterly N2 - Relations between discrete and continuous complexity models are considered. The present paper is devoted to combine both models. In particular we analyze the 3-Satisfiability problem. The existence of fast decision procedures for this problem over the reals is examined based on certain conditions on the discrete setting. Moreover we study the behaviour of exponential time computations over the reals depending on the real complexity of 3-Satisfiability. This will be done using tools from complexity theory over the integers. KW - Real model of computation KW - 3-Satisfiability KW - Sparseness KW - Exponential-time computations Y1 - 1995 UR - http://onlinelibrary.wiley.com/doi/10.1002/malq.19950410214/abstract U6 - https://doi.org/10.1002/malq.19950410214 SN - 0885-064X VL - 41 IS - 2 SP - 281 EP - 286 ER - TY - GEN A1 - Meer, Klaus A1 - Lickteig, Thomas T1 - A note on testing the resultant T2 - Journal of Complexity N2 - Shub (in "From Topology to Computation: Proceedings of the Smalefest." (M. Hirsch, J. Marsden, and M. Shub, Eds.), pp. 281-301, Springer-Verlag, New York/Berlin, 1993) proposes to attack the complex PFull-size image (<1 K) versus the NPFull-size image (<1 K) problem by focussing on lower bounds on testing the resultant of quadratic forms for zero. Taking up this question we show in the present paper a lower bound of order n3 for the resultant. Y1 - 1995 UR - http://www.sciencedirect.com/science/article/pii/S0885064X85710163?np=y U6 - https://doi.org/10.1006/jcom.1995.1016 SN - 0885-064X VL - 11 IS - 3 SP - 344 EP - 351 ER - TY - CHAP A1 - Meer, Klaus A1 - Schreiber, Harold T1 - Maßsynthese vier- sechs- und achtgliedriger ebener Kurbelgetriebe und ihre Anwendung im Kfz-Karosseriebau T2 - Kurvengetriebe, Koppelgetriebe, gesteuerte Antriebe, Problemlösungen in der Bewegungstechnik, Conference Veitshöchheim 26. and 27. September 2000, VDI-Getriebetagung 2000 Y1 - 2000 SN - 3-18-091567-6 SP - 277 EP - 297 PB - VDI Verlag CY - Düsseldorf ER - TY - CHAP A1 - Makowsky, Janos A. A1 - Meer, Klaus ED - Clote, Peter ED - Schwichtenberg, Helmut T1 - On the complexity of combinatorial and metafinite generating functions T2 - Computer science logic, 14th international workshop, proceedings, CSL 2000, Fischbachau, Germany, August 21 - 26, 2000 Y1 - 2000 SN - 3-540-67895-6 SP - 399 EP - 410 PB - Springer CY - Berlin [u.a.] ER - TY - CHAP A1 - Makowsky, Janos A. A1 - Meer, Klaus T1 - Polynomials of bounded tree-width T2 - Formal Power Series and Algebraic Combinatorics, Proceedings of the 12th International Conference, FPSAC'00, Moscow, Russia, June 2000 Y1 - 2000 SN - 3-540-67247-8 SP - 692 EP - 703 PB - Springer CY - Berlin [u.a.] ER - TY - GEN A1 - Meer, Klaus T1 - Counting problems over the reals. T2 - Theoretical Computer Science Y1 - 2000 SN - 0304-397 VL - 242 IS - 1-2 SP - 41 EP - 58 ER - TY - GEN A1 - Ben-David, Shai A1 - Meer, Klaus A1 - Michaux, Christian T1 - A note on non-complete problems in NP_R. T2 - Journal of Complexity Y1 - 2000 SN - 0885-064X VL - 16 IS - 1 SP - 324 EP - 332 ER - TY - CHAP A1 - Meer, Klaus ED - Dongarra, Jack T1 - On the Approximation of Interval Functions T2 - Applied Parallel Computing. State of the Art in Scientific Computing, 7th International Workshop, PARA 2004, Lyngby, Denmark, June 20-23, 2004, Revised Selected Papers Y1 - 2004 SN - 978-3-540-29067-4 SP - 169 EP - 178 PB - Springer CY - Heidelberg [u.a.] ER - TY - CHAP A1 - Meer, Klaus T1 - On consistency and width notions for constraint programs with algebraic constraints T2 - Functional and logic programming, 6th international symposium, proceedings, FLOPS 2002, Aizu, Japan, September 15 - 17, 2002 Y1 - 2002 SN - 3-540-44233-2 SP - 88 EP - 102 PB - Springer CY - Berlin [u.a.] ER - TY - GEN A1 - Gori, Marco A1 - Meer, Klaus T1 - A step towards a complexity theory for analog systems. T2 - Mathematical Logic Quarterly Y1 - 2002 SN - 0942-5616 VL - 48 IS - Suppl. 1 SP - 45 EP - 58 ER - TY - CHAP A1 - Makowsky, Janos A. A1 - Meer, Klaus ED - Cucker, Felipe ED - Rojas, Maurice T1 - Polynomials of bounded treewidth T2 - Foundations of Computational Mathematics, Proceedings of the Smalefest 2000 Y1 - 2002 SN - 978-981-02-4845-1 SP - 211 EP - 250 PB - World Scientific CY - Singapore ER - TY - GEN A1 - Matamala, Martin A1 - Meer, Klaus T1 - On the computational structure of the connected components of difficult sets T2 - Information Processing Letters Y1 - 1999 SN - 0020-0190 VL - 72 IS - 3-4 SP - 83 EP - 90 ER - TY - GEN A1 - Cucker, Felipe A1 - Meer, Klaus T1 - Logics which capture complexity classes over the reals T2 - Journal of Symbolic Logic Y1 - 1999 SN - 0022-4812 VL - 64 IS - 1 SP - 363 EP - 390 ER - TY - CHAP A1 - Cucker, Felipe A1 - Meer, Klaus T1 - Logics which capture complexity classes over the reals T2 - Mathematical Foundations of Computer Science 1997, 22nd International Symposium, MFCS '97 Bratislava, Slovakia, August 25-29, 1997 Proceedings Y1 - 1997 SP - 398 EP - 407 PB - Springer CY - Heidelberg ER - TY - CHAP A1 - Grädel, Erich A1 - Meer, Klaus T1 - Descriptive Complexity Theory over the real numbers T2 - Proceedings of the 27th Annual ACM Symposium on Theory of Computing STOC, Las Vegas, 1995 Y1 - 1995 U6 - https://doi.org/10.1145/225058.225151 SP - 315 EP - 324 PB - ACM CY - New York, NY ER - TY - GEN A1 - Benning, Wilhelm A1 - Elkoushy, Ashraf A1 - Meer, Klaus T1 - Innere-Punkt Methoden für die automatisierte Fehlersuche in geodätischen Anwendungen (Interior point methods for automatic blunders detection in surveying) T2 - Allgemeine Vermessungsnachrichten Y1 - 1997 SN - 0002-5968 VL - 104 IS - 8-9 SP - 319 EP - 324 ER - TY - GEN A1 - Meer, Klaus A1 - Michaux, Christian T1 - A Survey on Real Structural Complexity Theory T2 - Bulletin of the Belgian Mathematical Society Simon Stevin Y1 - 1997 SN - 1370-1444 VL - 4 IS - 1 SP - 113 EP - 148 ER - TY - CHAP A1 - Baartse, Martijn A1 - Meer, Klaus ED - Faliszewski, Piotr ED - Muscholl, Anca ED - Niedermeier, Rolf T1 - Real Interactive Proofs for VPSPACE T2 - 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016) Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0030-drops-64300 SN - 978-3-95977-016-3 SP - 14.1 EP - 14.13 PB - Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH CY - Wadern ER - TY - GEN A1 - Baartse, Martijn A1 - Meer, Klaus T1 - An algebraic proof of the real number PCP theorem T2 - Journal of Complexity N2 - The PCP theorem has recently been shown to hold as well in the real number model of Blum, Shub, and Smale (Baartse and Meer, 2015). The proof given there structurally closely follows the proof of the original PCP theorem by Dinur (2007). In this paper we show that the theorem also can be derived using algebraic techniques similar to those employed by Arora et al. (Arora et al., 1998; Arora and Safra, 1998) in the first proof of the PCP theorem. This needs considerable additional efforts. Due to severe problems when using low degree algebraic polynomials over the reals as codewords for one of the verifiers to be constructed, we work with certain trigonometric polynomials. This entails the necessity to design new segmentation procedures in order to obtain well structured real verifiers appropriate for applying the classical technique of verifier composition. We believe that designing as well an algebraic proof for the real PCP theorem on one side leads to interesting questions in real number complexity theory and on the other sheds light on which ingredients are necessary in order to prove an important result as the PCP theorem in different computational models. KW - Probabilistically checkable proofs KW - Real number model of computation KW - PCP theorem for NP over the reals KW - Testing trigonometric polynomials KW - Algebraic proofs Y1 - 2017 UR - http://www.sciencedirect.com/science/article/pii/S0885064X1630111X U6 - https://doi.org/10.1016/j.jco.2016.11.006 SN - 0885-064X VL - 40 SP - 34 EP - 77 ER - TY - GEN A1 - Baartse, Martijn A1 - Meer, Klaus T1 - Interactive proofs and a Shamir-like result for real number computations T2 - Computational Complexity Y1 - 2018 U6 - https://doi.org/10.1007/s00037-018-0174-6 SN - 1016-3328 SN - 1420-8954 ER -