@misc{MalajovichMeer, author = {Malajovich, Gregorio and Meer, Klaus}, title = {Computing Minimal Multi-Homogeneous B{\´e}zout Numbers Is Hard}, series = {Theory of Computing Systems}, volume = {40}, journal = {Theory of Computing Systems}, number = {4}, issn = {1432-4350}, pages = {553 -- 570}, language = {en} } @misc{Meer, author = {Meer, Klaus}, title = {On some relations between approximation and PCPs over the real numbers}, series = {Theory of Computing Systems}, volume = {41}, journal = {Theory of Computing Systems}, number = {1}, issn = {1432-4350}, pages = {107 -- 118}, language = {en} } @misc{FlarupHansenMeer, author = {Flarup Hansen, Uffe and Meer, Klaus}, title = {Two logical hierarchies of optimization problems over the real numbers}, series = {Mathematical Logic Quaterly}, volume = {52}, journal = {Mathematical Logic Quaterly}, number = {1}, issn = {0942-5616}, pages = {37 -- 50}, language = {en} } @misc{Meer, author = {Meer, Klaus}, title = {Transparent long proofs: A first PCP Theorem for NP(R)}, series = {Foundations of Computational Mathematics}, volume = {5}, journal = {Foundations of Computational Mathematics}, number = {3}, issn = {1615-3375}, pages = {231 -- 255}, language = {en} } @misc{Meer, author = {Meer, Klaus}, title = {Probabilistically checkable proofs over the reals}, series = {Electronic notes in theoretical computer science : ENTCS}, volume = {123}, journal = {Electronic notes in theoretical computer science : ENTCS}, issn = {1571-0661}, pages = {165 -- 177}, language = {en} } @misc{Meer, author = {Meer, Klaus}, title = {On a refined analysis of some problems in interval arithmetic using real number complexity theory}, series = {Reliable Computing}, volume = {10}, journal = {Reliable Computing}, number = {3}, issn = {1385-3139}, pages = {209 -- 225}, language = {en} } @inproceedings{GoriMeer, author = {Gori, Marco and Meer, Klaus}, title = {Some aspects of a complexity theory for continuous time systems}, series = {Extended abstract, Proceedings Computability in Europe, CiE 2007, Siena, Italy, June 18 - 23, 2007}, booktitle = {Extended abstract, Proceedings Computability in Europe, CiE 2007, Siena, Italy, June 18 - 23, 2007}, editor = {Cooper, Stuart Barry}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-540-73000-2}, pages = {554 -- 565}, language = {en} } @inproceedings{MeerRautenbach, author = {Meer, Klaus and Rautenbach, Dieter}, title = {On the OBDD size for graphs of bounded tree- and clique-width}, series = {Parameterized and exact computation, Second International Workshop, IWPEC 2006, Z{\"u}rich, Switzerland, September 13 - 15, 2006}, booktitle = {Parameterized and exact computation, Second International Workshop, IWPEC 2006, Z{\"u}rich, Switzerland, September 13 - 15, 2006}, editor = {Bodlaender, Hans L.}, publisher = {Springer}, address = {Berlin [u.a.]}, isbn = {978-3-540-39098-5}, pages = {72 -- 83}, language = {en} } @inproceedings{FlarupHansenMeer, author = {Flarup Hansen, Uffe and Meer, Klaus}, title = {Approximation classes for real number optimization problems}, series = {Extended abstract, 5th International conference on Unconventional Computation, York, UK, September 4-8, 2006}, booktitle = {Extended abstract, 5th International conference on Unconventional Computation, York, UK, September 4-8, 2006}, editor = {Calude, Cristian}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-540-38593-6}, pages = {86 -- 100}, language = {en} } @inproceedings{Zheng, author = {Zheng, Xizhong}, title = {A Computability Theory of Real Numbers}, series = {CCA 2008, August 21 - 24, 2008, Hagen, Germany}, booktitle = {CCA 2008, August 21 - 24, 2008, Hagen, Germany}, editor = {Brattka, Vasco}, publisher = {Hagen}, address = {Fernuniv.}, language = {en} } @inproceedings{Meer, author = {Meer, Klaus}, title = {On Ladner's Result for a Class of Real Machines with Restricted use of Constants}, series = {5th Conference on Computability in Europe, CiE 2009, Heidelberg, Germany, July 19 - 24, 2009}, booktitle = {5th Conference on Computability in Europe, CiE 2009, Heidelberg, Germany, July 19 - 24, 2009}, editor = {Ambos-Spies, Klaus}, publisher = {Springer}, address = {Heidelber [u.a.]}, isbn = {978-3-642-03072-7}, pages = {352 -- 361}, language = {en} } @inproceedings{RettingerZheng, author = {Rettinger, Robert and Zheng, Xizhong}, title = {Points on Computable Curves of Computable Lengths}, language = {en} } @inproceedings{RettingerZheng, author = {Rettinger, Robert and Zheng, Xizhong}, title = {On the Computability of the Rectifiable Simple Curves}, language = {en} } @misc{Meer, author = {Meer, Klaus}, title = {Fragestellungen aus Mathematik und theoretischer Informatik bei der Konstruktion von Getrieben}, series = {Forum der Forschung}, volume = {12}, journal = {Forum der Forschung}, number = {21}, issn = {0947-6989}, pages = {145 -- 150}, language = {de} } @article{Zheng, author = {Zheng, Xizhong}, title = {Classification of Computably Approximable Real Numbers}, language = {en} } @article{Zheng, author = {Zheng, Xizhong}, title = {A Hierarchy of Computably Enumerable Reals}, language = {en} } @misc{MeerZiegler, author = {Meer, Klaus and Ziegler, Martin}, title = {Real Computational Universality: The word problem for a class of groups with infinite presentation}, language = {en} } @inproceedings{KoiranMeer, author = {Koiran, Pascal and Meer, Klaus}, title = {On the Expressive Power of CNF Formulas of Bounded Tree- and Clique-Width}, series = {Graph-theoretic concepts in computer science, 34th international workshop, WG 2008, Durham, UK, June 30-July 2, 2008}, booktitle = {Graph-theoretic concepts in computer science, 34th international workshop, WG 2008, Durham, UK, June 30-July 2, 2008}, publisher = {Springer}, address = {Berlin [u.a.]}, isbn = {978-3-540-92247-6}, pages = {252 -- 263}, language = {en} } @misc{KoiranMeerBriquel, author = {Koiran, Pascal and Meer, Klaus and Briquel, Ir{\´e}n{\´e}e}, title = {On the Expressive Power of CNF Formulas of Bounded Tree- and Clique-Width}, language = {en} } @misc{Meer, author = {Meer, Klaus}, title = {Treewidth in Algebraic Complexity}, language = {en} } @inproceedings{Meer, author = {Meer, Klaus}, title = {An Extended Tree-Width Notion for Directed Graphs Related to the Computation of Permanents}, language = {en} } @inproceedings{NoackRotta, author = {Noack, Andreas and Rotta, Randolf}, title = {Multi-level Algorithms for Modularity Clustering}, abstract = {Modularity is a widely used quality measure for graph clusterings. Its exact maximization is prohibitively expensive for large graphs. Popular heuristics progressively merge clusters starting from singletons (coarsening), and optionally improve the resulting clustering by moving vertices between clusters (refinement). This paper experimentally compares existing and new heuristics of this type with respect to their effectiveness (achieved modularity) and runtime. For coarsening, it turns out that the most widely used criterion for merging clusters (modularity increase) is outperformed by other simple criteria, and that a recent multi-step algorithm is no improvement over simple single-step coarsening for these criteria. For refinement, a new multi-level algorithm produces significantly better clusterings than conventional single-level algorithms. A comparison with published benchmark results and algorithm implementations shows that combinations of coarsening and multi-level refinement are competitive with the best algorithms in the literature.}, language = {en} } @inproceedings{Meer, author = {Meer, Klaus}, title = {Almost transparent short proof for NP?}, series = {Extended abstract, Proceedings 18th International Symposium on Fundamentals of Computation Theory FCT 2011, Oslo, 2011}, booktitle = {Extended abstract, Proceedings 18th International Symposium on Fundamentals of Computation Theory FCT 2011, Oslo, 2011}, isbn = {978-3-642-22952-7}, pages = {41 -- 52}, language = {en} } @misc{RottaNoack, author = {Rotta, Randolf and Noack, Andreas}, title = {Multilevel local search algorithms for modularity clusterin}, series = {Journal on Experimental Algorithmics}, volume = {16}, journal = {Journal on Experimental Algorithmics}, number = {2}, issn = {1084-6654}, language = {en} } @misc{Meer, author = {Meer, Klaus}, title = {On Ladnerʼs result for a class of real machines with restricted use of constants}, series = {Information and Computation}, volume = {210}, journal = {Information and Computation}, issn = {0890-5401}, pages = {13 -- 20}, language = {en} } @misc{RottaPrescherTraueetal., author = {Rotta, Randolf and Prescher, Thomas and Traue, Jana and Nolte, J{\"o}rg}, title = {Data Sharing Mechanisms for Parallel Graph Algorithms on the Intel SCC}, series = {MARC Symposium at ONERA'2012, July 19th-20th 2012, Toulouse, Frankreich}, journal = {MARC Symposium at ONERA'2012, July 19th-20th 2012, Toulouse, Frankreich}, isbn = {978-2-7257-0016-8}, pages = {13 -- 18}, language = {en} } @misc{BaartseBarmpalias, author = {Baartse, Martijn and Barmpalias, George}, title = {On the gap between trivial and nontrivial initial segment prefix-free complexity}, series = {Theory of Computing Systems}, journal = {Theory of Computing Systems}, issn = {1433-0490}, pages = {20}, abstract = {An infinite sequence X is said to have trivial (prefix-free) initial segment complexity if the prefix-free Kolmogorov complexity of each initial segment of X is the same as the complexity of the sequence of 0s of the same length, up to a constant. We study the gap between the minimum complexity K(0 n ) and the initial segment complexity of a nontrivial sequence, and in particular the nondecreasing unbounded functions f such that (⋆) for a nontrivial sequence X, where K denotes the prefix-free complexity. Our first result is that there exists a \$\varDelta^{0}_{3}\$ unbounded nondecreasing function f which does not have this property. It is known that such functions cannot be \$\varDelta^{0}_{2}\$ hence this is an optimal bound on their arithmetical complexity. Moreover it improves the bound \$\varDelta^{0}_{4}\$ that was known from Csima and Montalb{\´a}n (Proc. Amer. Math. Soc. 134(5):1499-1502, 2006). Our second result is that if f is \$\varDelta^{0}_{2}\$ then there exists a non-empty \$\varPi^{0}_{1}\$ class of reals X with nontrivial prefix-free complexity which satisfy (⋆). This implies that in this case there uncountably many nontrivial reals X satisfying (⋆) in various well known classes from computability theory and algorithmic randomness; for example low for Ω, non-low for Ω and computably dominated reals. A special case of this result was independently obtained by Bienvenu, Merkle and Nies (STACS, pp. 452-463, 2011).}, language = {en} } @misc{RottaBuechnerNolte, author = {Rotta, Randolf and B{\"u}chner, Steffen and Nolte, J{\"o}rg}, title = {Middleware for Many-Cores - Why It Is Needed and What Functionality It Should Provide}, series = {4th USENIX Workshop on Hot Topics in Parallelism (HotPar '12), Berkeley, 2012}, journal = {4th USENIX Workshop on Hot Topics in Parallelism (HotPar '12), Berkeley, 2012}, abstract = {Today's multi-cores and future many-cores are NUMA architectures with complex cache hierarchies and multiple memory channels. Depending on the topologies of these memory networks we find everything from true data sharing with shared caches to distributed memory architectures which just pretend to be physical shared memory systems. In fact, most many-cores are hybrid systems that exhibit the characteristics of both distributed systems and SMPs. In this paper we argue in favor of middleware platforms for many-cores. We will discuss the needed functionality in contrast to common distributed system middleware and present micro benchmarks on several architectures to substantiate our claims.}, language = {en} } @misc{RottaPrescherTraueetal., author = {Rotta, Randolf and Prescher, Thomas and Traue, Jana and Nolte, J{\"o}rg}, title = {In-Memory Communication Mechanisms for Many-Cores - Experiences with the Intel SCC}, series = {TACC-Intel Highly Parallel Computing Symposium (TIHPCS), Austin/Texas, 2012}, journal = {TACC-Intel Highly Parallel Computing Symposium (TIHPCS), Austin/Texas, 2012}, abstract = {Many-core processors combine fast on-chip communication with access to large amounts of shared memory. This makes it possible to exploit the benefits of distributed as well as shared memory programming models within single parallel algorithms. While large amounts of data can be shared in the memory and caches, coordinating the activities of hundreds of cores relies on cross core communication mechanisms with ultra low latency for very small messages. In this paper we discuss two communication protocols for the Intel SCC and compare them to the MPI implementation of the SCC. Our micro-benchmark results underline that special purpose protocols for small messages make much finer levels of parallelism possible than general purpose message passing systems. Index Terms—many-core, message passing, shared memory}, language = {en} } @inproceedings{MeerBaartse, author = {Meer, Klaus and Baartse, Martijn}, title = {The PCP theorem for NP over the reals}, series = {30th Symposium on Theoretical Aspects of Computer Science STACS , Kiel, 2013}, booktitle = {30th Symposium on Theoretical Aspects of Computer Science STACS , Kiel, 2013}, address = {Leibnitz}, doi = {10.4230/LIPIcs.STACS.2013.104}, url = {http://nbn-resolving.de/urn:nbn:de:0030-drops-39262}, pages = {104 -- 115}, language = {en} } @misc{Meer, author = {Meer, Klaus}, title = {Some initial thoughts on bounded query computations over the reals}, series = {International Journal of Foundations of Computer Science}, volume = {23}, journal = {International Journal of Foundations of Computer Science}, number = {7}, issn = {0129-0541}, doi = {10.1142/S0129054112400618}, pages = {1499 -- 1510}, language = {en} } @inproceedings{Meer, author = {Meer, Klaus}, title = {On the complexity of some problems in interval arithmetic}, series = {Proceedings, 28th International Symposium on Mathematical Foundations of Computer Science, Bratislava, Slovakia, 2003}, booktitle = {Proceedings, 28th International Symposium on Mathematical Foundations of Computer Science, Bratislava, Slovakia, 2003}, publisher = {Springer}, address = {Berlin [u.a.]}, isbn = {3-540-40671-9}, pages = {582 -- 591}, language = {en} } @incollection{JongenMeer, author = {Jongen, Hubertus Theodor and Meer, Klaus}, title = {Das Simplexverfahren}, series = {Lexikon der Mathematik, Band 5}, booktitle = {Lexikon der Mathematik, Band 5}, editor = {Walz, Guido}, publisher = {Spektrum Akademischer Verlag}, address = {Heidelberg}, isbn = {3-8274-0437-1}, pages = {27 -- 30}, language = {de} } @incollection{JongenMeer, author = {Jongen, Hubertus Theodor and Meer, Klaus}, title = {Ellipsoidmethoden}, series = {Lexikon der Mathematik, Band 2}, booktitle = {Lexikon der Mathematik, Band 2}, editor = {Walz, Guido}, publisher = {Spektrum Akademischer Verlag}, address = {Heidelberg}, isbn = {3-8274-0434-7}, pages = {37 -- 38}, language = {de} } @incollection{JongenMeer, author = {Jongen, Hubertus Theodor and Meer, Klaus}, title = {Innere-Punkte Methoden}, series = {Lexikon der Mathematik, Band 2}, booktitle = {Lexikon der Mathematik, Band 2}, editor = {Walz, Guido}, publisher = {Spektrum Akademischer Verlag}, address = {Heidelberg}, isbn = {3-8274-0434-7}, pages = {491 -- 494}, language = {de} } @misc{Meer, author = {Meer, Klaus}, title = {An Extended Tree-Width Notion for Directed Graphs Related to the Computation of Permanents}, series = {Theory of Computing Systems}, volume = {55}, journal = {Theory of Computing Systems}, number = {2}, issn = {1432-4350}, pages = {330 -- 346}, language = {en} } @inproceedings{LickteigMeerPardo, author = {Lickteig, Thomas and Meer, Klaus and Pardo, Luis Miguel}, title = {Real Computation and Complexity, Dagstuhl seminar}, publisher = {Internationale Begegnungs- und Forschungszentrum f{\"u}r Informatik}, address = {Dagstuhl}, url = {http://nbn-resolving.de/urn:nbn:de:0030-drops-4994}, language = {en} } @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} } @inproceedings{MeerBaartse, author = {Meer, Klaus and Baartse, Martijn}, title = {Testing Low Degree Trigonometric Polynomials}, series = {Computer Science - Theory and Applications 9th International Computer Science Symposium in Russia, CSR 2014, Moscow, Russia, June 7-11, 2014, Proceedings}, booktitle = {Computer Science - Theory and Applications 9th International Computer Science Symposium in Russia, CSR 2014, Moscow, Russia, June 7-11, 2014, Proceedings}, editor = {Hirsch, Edward and Kuznetsov, Sergei O. and Pin, Jean-{\´E}ric and Vereshchagin, Nikolay}, publisher = {Springer International Publishing}, address = {Berlin [u.a.]}, isbn = {978-3-319-06685-1}, doi = {10.1007/978-3-319-06686-8}, pages = {77 -- 96}, language = {en} } @inproceedings{MeerNaif, author = {Meer, Klaus and Naif, Ameen}, title = {Periodic Generalized Automata over the Reals}, series = {Language and Automata Theory and Applications 10th International Conference, LATA 2016, Prague, Czech Republic, March 14-18, 2016, Proceedings}, booktitle = {Language and Automata Theory and Applications 10th International Conference, LATA 2016, Prague, Czech Republic, March 14-18, 2016, Proceedings}, editor = {Dediu, Adrian-Horia and Janoušek, Jan and Mart{\´i}n-Vide, Carlos and Truthe, Bianca}, publisher = {Springer International Publishing}, address = {Berlin [u.a.]}, isbn = {978-3-319-29999-0}, doi = {10.1007/978-3-319-30000-9}, pages = {168 -- 180}, language = {en} } @misc{MeerLickteig, author = {Meer, Klaus and Lickteig, Thomas}, title = {Semi-algebraic complexity - Additive complexity of matrix computational tasks}, series = {Journal of Complexity}, volume = {13}, journal = {Journal of Complexity}, number = {1}, issn = {0885-064X}, doi = {10.1006/jcom.1997.0430}, pages = {83 -- 107}, abstract = {This paper is devoted to the study of lower bounds on the inherent number of additions and subtractions necessary to solve some natural matrix computational tasks such as computing the nullspace, some band transformation, and some triangulation of a givenm×mmatrix. The additive complexities of such tasks are shown to grow asymptotically like that of them×mmatrix multiplication. The paper is a continuation of an earlier paper by the authors, and also of 4where multiplicative complexity has been considered. We also propose a formalization of semialgebraic computational tasks.}, language = {en} } @misc{MeerMalajovich, author = {Meer, Klaus and Malajovich, Gregorio}, title = {On the structure of NP_C}, series = {SIAM Journal on Computing}, volume = {28}, journal = {SIAM Journal on Computing}, number = {1}, issn = {1095-7111}, doi = {10.1137/S0097539795294980}, pages = {27 -- 35}, language = {en} } @inproceedings{Meer, author = {Meer, Klaus}, title = {Counting problems over the reals}, series = {Mathematical foundations of computer science 1997, 22nd international symposium, proceedings, MFCS '97, Bratislava, Slovakia, August 25 - 29, 1997}, booktitle = {Mathematical foundations of computer science 1997, 22nd international symposium, proceedings, MFCS '97, Bratislava, Slovakia, August 25 - 29, 1997}, editor = {Pr{\´i}vara, Igor and Ružička, Peter}, publisher = {Springer}, address = {Berlin [u.a.]}, isbn = {978-3-540-63437-9}, doi = {10.1007/BFb0029983}, pages = {398 -- 407}, abstract = {In this paper we introduce a complexity theoretic notion of counting problems over the real numbers. We follow the approaches of Blum, Shub, and Smale.}, language = {en} }