Publikationen

1. Elementary theories of valued fields, Dissertation (Ph. D. thesis), Universität Heidelberg, 1971.
2. Infinitary model theoretic properties of kappa-saturated structures, Zeitschrift Mathematische Logik und Grundlagen der Mathematik 19 (1973), pp. 97-109.
3. Two model theoretic proofs of Rückert's Nullstellensatz, Trans. AMS 203 (1975), pp. 331-342.
4. Commutative regular rings without prime model extensions (with D. Saracino), Proceeding AMS 47 (1975), pp. 201-207.
5. Model-completeness and elimination of quantifiers for subdirect products of structures, Journal of Algebra 36 (1975), pp. 252-277.
6. On algebraic curves over commutative regular rings (with D. Saracino), in Model Theory and Algebra, Springer LNM vol. 498 (1975), pp. 307-383.
7. Negative-existentially complete structures and definability in free extensions, Journal of Symbolic Logic 41 (1976), pp. 95-108.
8. On the elementary theory of Hensel fields, Annals of mathematical Logic 10 (1976), pp. 59-93.
9. Nullstellensätze - a model theoretic framework, Zeitschrift Mathematische Logik und Grundlagen der Mathematik 23 (1977), pp. 539-545.
10. A note on aleph0-categorical model companions, Archiv für mathematische Logik 19 (1978), pp. 23-29.
11. Model theory of lattice products, Habilitationsschrift, Universität Heidelberg (235 pp.).
12. Lattice products, in Logic Colloquium 1978, Mons, North-Holland, Amsterdam, pp. 423-426.
13. The model theoretic significance of complemented existential formulas, Journal of Symbolic Logic 46 (1981), pp. 843-849.
14. Quantifier elimination for certain ordered and lattice-ordered abelian groups, Bull. Soc. Math. Belg. 33, ser. B (1981), pp. 131-156.
15. Model theory and lattices of formulas, in Logic Colloquium '80 , Patras, North-Holland, Amsterdam.
16. Valuation rings and boolean products, Proc. Conf. F.N.R.S., Bruxelles, 1982.
17. Quantifier elimination for modules, Archiv für mathematische Logik 25 (1985), pp. 1-11.
18. Quantifier elimination for distributive lattices and measure algebras, Zeitschrift für mathematische Logik und Grundlagen der Mathematik, 31 (1985), pp. 249-261.
19. Aspects of quantifier elimination in algebra, in Universal Algebra and its links with logic ..., Proc. 25, Arbeitstagung Darmstadt 1983, Heldermann V., Berlin, pp. 85-105.
20. Quantifier elimination and decision procedures for valued fields, in Models and Sets, Proc. Logic Coll. '83, Aachen, part 1, Springer LNM vol. 1103, pp. 419-472.
21. Existentially closed semilattices, Algebra Universalis 21 (1985), pp. 146-155.
22. The complexity of linear problems in fields, Journal of Symbolic Computation 5 (1988), pp. 3-27.
23. The complexity of elementary problems in archimedean ordered groups, Extended abstract, in EUROCAL '85, Linz, Springer LNCS vol. 204, pp. 87-88.
24. Quantifier eliminable ordered abelian groups, in Algebra and Order, S. Wolfenstein Ed., Luminy 1984, Heldermann Verlag, pp. 113-126.
25. Efficient decision algorithms for locally finite theories, in Proc. AAECC-3 conference, Grenoble, 1985, Springer LNCS vol. 229, pp. 262-273.
26. Model theory of abelian lattice-ordered groups, in Lattice-Ordered Groups, A.M.W. Glass and W.C. Holland (eds.), Kluwer Academic Publishers, 1989, pp. 41-79.
27. The complexity of the word problem for abelian l-groups, Theor. Comp. Sci. 48 (1986), pp. 127-132.
28. Diamond formulas in the dynamic logic of recursively enumerable programms, in Proc. CADE-8, Oxford 1986, Springer LNCS vol. 230, pp. 564-571.
29. Computing dimension and independent sets for polynomial ideals (with H. Kredel), Journal of Symbolic Computation 6 (1988), pp. 231-247.
30. The complexity of almost linear diophantine problems, Journal of Symbolic Computation 10 (1990), pp. 395-403.
31. Non-commutative Gröbner bases in algebras of solvable type (with A. Kandri-Rody), Journal of Symbolic Computation 9 (1990), pp. 1-26.
32. Some bounds for the construction of Gröbner bases, in Proc. AAECC-4, Karlsruhe 1986, Springer LNCS vol. 307, pp. 195-201.
33. Gröbner bases for polynomial ideals over commutative regular rings, in Proc. EUROCAL '87, Leipzig, Springer LNCS vol. 378, pp. 336-347.
34. Admissible orders and linear forms, ACM SIGSAM Bull. 21 (1987), pp. 16-18.
35. Efficient decision procedures for locally finite theories II, in Proc. ISSAC 88, Rom, 1988, Springer LNCS vol. 358, pp. 390-401.
36. Continuous functions: l-groups and decision problems (with Shen Fuxing), preliminary report, Feb. 87, Universität Heidelberg.
37. Riesz groups and existentially closed abelian po-groups, preliminary report, March 1987, Universität Heidelberg.
38. Constructing Universal Gröbner bases, in Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, Proc. AAECC-5, L. Huguet (Ed.), Springer LNCS, vol. 356, pp. 408-417.
39. Existential equivalence of ordered abelian groups with parameters, MIP-8911, Universität Passau, March 1989. Archive for Math. Logic, 29 (1990), pp. 237-248.
40. Comprehensive Gröbner bases, MIP-9003, Universität Passau, 1990, Journal of Symbolic Computation 14 (1992), pp. 1-29.
41. Parametric Gröbner bases in rings of solvable type (with H. Kredel), MIP-9006 Universität Passau 1990, Proc. IV. International Conference on Computer Algebra in Physical Research, Joint Institute for Nuclear Research Dubna, USSR, May 1990, World Scientific, Singapore, 1991, pp. 236-244.
42. On the number of term orders (with G. Ritter), MIP-9014, Universität Passau 1990, J. AAECC, vol. 2 (1991), pp. 55-79.
43. The Chinese remainder problem, multivariate interpolation, and Gröbner bases (with Th. Becker), MIP-9103, Universität Passau 1991, Proc. ISSAC 91, S.M. Watt, Ed., pp. 64-69.
44. Finite Gröbner bases in non-Noetherian skew polynomial rings, Proc. ISSAC 92, Berkeley, USA, July 1993, pp. 329-334.
45. Applying linear quantifier elimination (with R. Loos), The Computer Journal, vol. 36, No. 5, 1993.
46. Differential term-orders, Proc. ISSAC 93, Kiew, ACM Press, 1993, pp. 245-253.
47. A new approach to quantifier elimination for real algebra, MIP-9305, Universität Passau, July 1993, Proc. Collins Symposium Linz, Oct. 1993, to appear.
48. Quantifier elimination for real algebra - the quadratic case and beyond, AAECC 8, 1997, pp. 85-101.
49. Quantifier elimination for real algebra - the cubic case, Proc. ISSAC 94, Oxford, 1994, ACM Press, pp. 258-263.
50. Parametric linear and quadratic optimization by elimination, MIP-9404, Universität Passau, April 1994, to appear in Journal of Symbolic Computation, 1997.
51. Erkenntnistheoretische Aspekte der Mathematik, Symposium "Rationalität der Wissenschaften", Universität Passau, Oktober 1993, printed Mai 1994.
52. Solving parametric polynomial equations and inequalities by symbolic algorithms, MIP-9504, Universität Passau, Januar 1995, in Proc. of the workshop "Computer Algebra in Science and Engineering", Bielefeld, August 1994, World Scientific, Singapore, 1995, pp. 163-179.
53. Parametric mixed integer programming by elimination (with Xue Rui), MIP-9503, Universität Passau, January 1995, poster presentation ISSAC 95, Montreal.
54. Simulation and optimization by quantifier elimination, MIP-9607 , Universität Passau, April 1996, Journal of Symbolic Computation 24 (1997), pp. 189-208, special issue on applications of quantifier elimination.
55. A new approach for automatic theorem proving in real geometry (with A. Dolzmann and Th. Sturm), MIP-9611, Universität Passau, May 1996, Journal of Automated Reasoning 21 (1998), pp. 357-380.
56. Complexity and uniformity of elimination in Presburger arithmetic, MIP-9703, Universität Passau, January 1997, Proc. ISSAC 97, ACM Press 1997, pp. 48-53.
57. Computational geometry problems in REDLOG (with Th. Sturm), MIP-9708, Universität Passau, April 1997, Automated Deduction in Geometry, selected papers from an international workshop in Toulouse 1996, D. Wang (ed.), pp. 58-86.
58. Rounding and blending of solids by a real elimination method (with Th. Sturm), Universität Passau, June 1997, in Proceedings 15. IMACS World Congress, Berlin, 1997, IMACS, Wissenschaft & Technik Verlag, pp. 727-732.
59. Real quantifier elimination in practice (with A. Dolzmann and Th. Sturm), MIP-9720, Universität Passau, December 1997, Algorithmic Algebra and Number Theory, Springer 1998, Matzat, B. H. and Greuel, G.-M. and Hiss, G. (ed.), pp. 221-247.
60. Automatisches Beweisen in der Geometrie, (with A. Dolzmann and Th. Sturm), Computeralgebra Rundbrief der Fachgruppe Computeralgebra der GI, DMV, GAMM, 23, 1998, pp. 15-18.
61. A New Approach to Quantifier Elimination for Real Algebra, in Quantifier Elimination and Cylindrical Algebraic Decomposition, Springer 1998, Caviness, B.F. and Johnson, J.R. (ed.), pp. 376-392.
62. Mixed Real-Integer Linear Quantifier Elimination, MIP-9814, Universität Passau, October 1998.
63. Mixed Real-Integer Linear Quantifier Elimination, extended version, MIP-9902, Universität Passau, January 1999, Proc. ISSAC'99, ACM-Press 1999, pp. 129-136.
64. Semilinear motion planning in REDLOG, MIP-9906, Universität Passau, May 1999. AAECC to appear.
65. Deciding Linear-Trigonometric Problems, (with H. Anai) MIP-0001, Universität Passau, February 2000, Proc. ISSAC'2000, ACM-Press 2000, pp. 14-22.
66. Local Quantifier Elimination, (with A. Dolzmann) MIP-0003, Universität Passau, February 2000, Proc. ISSAC'2000, ACM-Press 2000, pp. 86-94.
67. Deciding Linear-Transcendental Problems, MIP-0005, Universität Passau, April 2000, Proc. CASC'2000, Springer Verlag 2000, pp. 423-437.
68. Solving Linear-Transcendental Problems, Proc. EACA'2000, Universidat Polytechnica de Catalunya, 2000, pp. 81-87 .
69. Reach set computations using real quantifier elimination (with H.Anai), Proceedings HSCC'2001, Hybrid Systems: Computation and Control, Springer LNCS 2034, pp. 63-76.
70. Semilinear motion planning among moving objects in REDLOG, in Computer Algebra in Scientific Computation - CASC 2001, Springer 2001, pp. 541-553.
71. Canonical Comprehensive Gröbner bases, Proceedings ISSAC'2002. ACM-Press, 2002, pp. 270-276.
72. Quantifier elimination in term algebras (with Th. Sturm), in Computer Algebra in Scientific Computation - CASC 2002, TUM, 2002, pp. 285-300.
73. Comprehensive Gröbner bases and regular rings, Proceedings LMCS'2002, RISC-Linz, 2002, pp. 256-264.
74. Canonical Comprehensive Gröbner bases, J. Symb. Comp. 36, 2003, pp. 669-683.
75. Gröbner Bases for Inexact Input Data, in Computer Algebra in Scientific Computation - CASC 2003, Passau, TUM, 2003, pp. 403-412.
76. Solving Constraints by Elimination Methods, in Automatic Reasoning, Proc. IJCAR, Cork, Ireland, July 2004, Springer LNAI 3097, 2004, pp. 669-683.
77. Gröbner Bases for Binomials with Parametric Exponents, in Computer Algebra in Scientific Computation - CASC 2004, St. Petersburg, TUM, 2004, pp. 467-478.
78. Solving Univariate P-adic Constraints (with Th. Sturm), in Computer Algebra in Scientific Computation - CASC 2004, St. Petersburg, TUM, 2004, pp. 437-450.

Books

1. Editor (with D. Saracino), Model Theory and Algebra, a memorial tribute to Abraham Robinson, Springer LNM, vol. 498, 1975.
2. Gröbner Bases -A computational approach to commutative algebra, Th. Becker/V. Weispfenning (in cooperation with Heinz Kredel), Graduate Texts in Mathematics, Springer, 1993. Second printing 1998.
3. Computeralgebra in Deutschland, Bestandsaufnahme, Möglichkeiten, Perspektiven, Passau und Heidelberg 1993 (Herausgegeben zusammen mit J. Grabmeier für die Fachgruppe Computeralgebra der GI, DMV und GAMM.) Vertrieb: DLGI, Bonn, 320 Seiten.
4. Computer Algebra Handbook, Editor together with J. Grabmeier and E. Kaltofen, Springer Verlag, 2003.
5. Algebra und Logik, Th. Sturm, V. Weispfenning, Lecture Notes, 2005.

Translation

1. Translation and Revision of "Turing Machines", J.E. Hopcroft, Scient. American, May 1984, for the German Edition Spektrum der Wissenschaft, July 1984.