@incollection{JongenMeer, author = {Jongen, Hubertus Theodor and Meer, Klaus}, title = {Optimierung}, series = {Faszination Mathematik}, booktitle = {Faszination Mathematik}, editor = {Walz, Guido}, publisher = {Spektrum Akademischer Verlag}, address = {Heidelberg}, isbn = {3-8274-1419-9}, pages = {211 -- 216}, language = {de} } @misc{Meer, author = {Meer, Klaus}, title = {Syropoulos, Apostolos: Hypercomputation. Berlin : Springer, 2008}, series = {AMS Mathematical Reviews}, journal = {AMS Mathematical Reviews}, number = {2009j}, issn = {0025-5629}, language = {en} } @inproceedings{MeerBaartse, author = {Meer, Klaus and Baartse, Martijn}, title = {Topics in Real and Complex Number Complexity Theory}, series = {Recent Advances in Real Complexity and Computation}, booktitle = {Recent Advances in Real Complexity and Computation}, editor = {Monta{\~n}a, Jos{\´e} Luis and Pardo, Luis Miguel}, publisher = {American Mathematical Society}, address = {Providence, RI}, isbn = {978-0-8218-9150-6}, doi = {10.1090/conm/604}, pages = {1 -- 53}, language = {en} } @misc{MeerSchmittSchreiber, author = {Meer, Klaus and Schmitt, Burkhard and Schreiber, Harold}, title = {Dimensional Synthesis of Planar Stephenson-Mechanisms for Motion Generation by Circlepoint Search and Homotopy Methods}, series = {Mechanism and Machine Theory}, volume = {37}, journal = {Mechanism and Machine Theory}, number = {7}, issn = {0094-114X}, doi = {10.1016/S0094-114X(02)00016-2}, pages = {717 -- 737}, abstract = {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 B{\´e}zout number and the BKK bound - will be compared.}, language = {en} } @misc{MeerWeber, author = {Meer, Klaus and Weber, Gerhard Wilhelm}, title = {Some aspects of studying an optimization or decision problem in different computational models}, series = {European Journal of Operational Research}, volume = {143}, journal = {European Journal of Operational Research}, number = {2}, issn = {0377-2217}, doi = {10.1016/S0377-2217(02)00269-2}, pages = {406 -- 418}, abstract = {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.}, language = {en} } @misc{Meer, author = {Meer, Klaus}, title = {Wegener, Ingo: Komplexit{\"a}tstheorie. Berlin : Springer, 2003}, series = {Jahresbericht der Deutschen Mathematiker-Vereinigung}, volume = {108}, journal = {Jahresbericht der Deutschen Mathematiker-Vereinigung}, number = {2}, issn = {0012-0456}, pages = {5 -- 8}, language = {de} } @misc{Meer, author = {Meer, Klaus}, title = {Blum, Lenore [u.a.]: Complexity and real computation. Berlin : Springer, 1998}, series = {AMS Mathematical Reviews}, journal = {AMS Mathematical Reviews}, number = {99a}, issn = {0025-5629}, pages = {509 -- 600}, language = {en} } @misc{OPUS4-15615, title = {Language, Life, Limits 10th Conference on Computability in Europe, CiE 2014, Budapest, Hungary, June 23-27, 2014, Proceedings}, editor = {Beckmann, Arnold and Csuhaj-Varj{\´u}, Erzs{\´e}bet and Meer, Klaus}, publisher = {Springer International Publishing}, address = {Berlin [u.a.]}, isbn = {978-3-319-08018-5}, doi = {10.1007/978-3-319-08019-2}, pages = {XIV, 410}, abstract = {This book constitutes the refereed proceedings of the 10th Conference on Computability in Europe, CiE 2014, held in Budapest, Hungary, in June 2014. The 42 revised papers presented were carefully reviewed and selected from 78 submissions and included together with 15 invited papers in this proceedings. The conference had six special sessions: computational linguistics, bio-inspired computation, history and philosophy of computing, computability theory, online algorithms and complexity in automata theory.}, language = {en} } @misc{MeerNaif, author = {Meer, Klaus and Naif, Ameen}, title = {Generalized finite automata over real and complex numbers}, series = {Theoretical Computer Science}, volume = {Vol. 591}, journal = {Theoretical Computer Science}, issn = {0304-3975}, doi = {10.1016/j.tcs.2015.05.001}, pages = {85 -- 98}, abstract = {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.}, language = {en} } @misc{MeerBaartse, author = {Meer, Klaus and Baartse, Martijn}, title = {The PCP theorem for NP over the reals}, series = {Foundations of Computational Mathematics}, volume = {15}, journal = {Foundations of Computational Mathematics}, number = {3}, issn = {1615-3375}, doi = {10.1007/s10208-014-9188-x}, pages = {651 -- 680}, language = {en} } @inproceedings{MeerBaartse, author = {Meer, Klaus and Baartse, Martijn}, title = {An algebraic proof of the real number PCP theorem}, series = {Mathematical Foundations of Computer Science 2015 40th International Symposium, MFCS 2015, Milan, Italy, August 24-28, 2015, Proceedings, Part II}, booktitle = {Mathematical Foundations of Computer Science 2015 40th International Symposium, MFCS 2015, Milan, Italy, August 24-28, 2015, Proceedings, Part II}, publisher = {Springer-Verlag}, address = {Berlin [u.a.]}, isbn = {978-3-662-48053-3}, doi = {10.1007/978-3-662-48054-0}, pages = {50 -- 61}, language = {en} } @inproceedings{MeerBaartse, author = {Meer, Klaus and Baartse, Martijn}, title = {Some results on interactive proofs for real computations}, series = {Evolving Computability 11th Conference on Computability in Europe, CiE 2015, Bucharest, Romania, June 29-July 3, 2015, Proceedings}, booktitle = {Evolving Computability 11th Conference on Computability in Europe, CiE 2015, Bucharest, Romania, June 29-July 3, 2015, Proceedings}, editor = {Beckmann, Arnold and Mitrana, Victor and Soskova, Mariya}, publisher = {Springer International Publishing}, address = {Berlin [u.a.]}, isbn = {978-3-319-20027-9}, doi = {10.1007/978-3-319-20028-6}, pages = {107 -- 116}, language = {en} } @inproceedings{MeerNaif, author = {Meer, Klaus and Naif, Ameen}, title = {Generalized Finite Automata over Real and Complex Numbers}, series = {Theory and Applications of Models of Computation 11th Annual Conference, TAMC 2014, Chennai, India, April 11-13, 2014, Proceedings}, booktitle = {Theory and Applications of Models of Computation 11th Annual Conference, TAMC 2014, Chennai, India, April 11-13, 2014, Proceedings}, editor = {Gopal, T. V. and Agrawal, Manindra and Li, Angsheng and Cooper, Stuart Barry}, publisher = {Springer International Publishing}, address = {Berlin [u.a.]}, isbn = {978-3-319-06088-0}, doi = {10.1007/978-3-319-06089-7}, pages = {168 -- 187}, language = {en} }