Bruno Buchberger

main contributions
refereed publications
unrefereed
books - journals
invited talks
contributed talks
 

 

Refereed Publications in Journals, Proceedings, etc.

Copyright: If you download papers, please, respect the copyright of the publishers indicated at the various papers. If no publisher is explicitly mentioned, the copyright is with Bruno Buchberger.

If you download a paper, I would appreciate if you send an e-mail to me with the title of the paper. If you use material from the papers, please, cite them appropriately.

The files with extension .nb are Mathematica notebooks. For reading them you need Mathematica installed, see Wolfram. For executing the formulae in the input cells in some of the papers, in addition to Mathematica, you need our Theorema system, see Theorema.

2005-09-09-A: Theorema: Towards Computer-Aided Mathematical Theory Exploration.
B. Buchberger, A. Craciun, T. Jebelean, L. Kovacs, T. Kutsia, K. Nakagawa, F. Piroi, N. Popov, J. Robu, M. Rosenkranz, W. Windsteiger
In: Journal of Applied Logic, pp. -. 2005.
ISSN 1570-8683.

[pdf]
2005-07-01-A: Label Management in Theorema.
F. Piroi, B. Buchberger.
In: Informal proceedings of the 4th International Conference on Mathematical Knowledge Management, M. Kohlhase (ed.), pp. -. July 2005. Bremen, Germany.

2004-09-26-A: Algorithm Synthesis by Lazy Thinking: Using Problem Schemes.
B. Buchberger, A. Craciun.
In: D.Petcu, V.Negru, D.Zaharie, T.Jebelean (eds) Proceedings of SYNASC 2004, 6th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing Timisoara, Romania, September 26-30, Mirton Publisher, pg. 90-106.
ISBN 973-661-441-7
Copyright: Mirton Publisher, Timisoara, Romania

[pdf]
2004-09-22-B: Proving and Constraint Solving in Computational Origami.
T. Ida, D. Tepeneu, B. Buchberger, J. Robu.
In: B. Buchberger, John Campbell (eds.) Proceedings of AISC 2004 (7 th International Conference on Artificial Intelligence and Symbolic Computation, September 22-24, 2004, RISC, Johannes Kepler University, Austria), Springer Lecture Notes in Artificial Intelligence, Vol. 3249, Springer, Berlin, Heidelberg, 2004.
ISSN 0302-9743, ISBN 3-540-23212-5
Copyright: Springer, Berlin

2004-09-22-A: Algorithm Supported Mathematical Theory Exploration.
B. Buchberger
In: B. Buchberger, John Campbell (eds.) Proceedings of AISC 2004 (7 th International Conference on Artificial Intelligence and Symbolic Computation, September 22-24, 2004, RISC, Johannes Kepler University, Austria), Springer Lecture Notes in Artificial Intelligence, Vol. 3249, Springer, Berlin, Heidelberg, 2004.
ISSN 0302-9743, ISBN 3-540-23212-5
Copyright: Springer, Berlin

[pdf]
2004-09-19-B: An Environment for Building Mathematical Knowledge Libraries.
F. Piroi, B. Buchberger
in A.Asperti, G.Bancerek, A.Trybulec (eds.): Proceedings of the Third International Conference on Mathematical Knowledge Management, MKM 2004, Bialowieza, POLAND, September 19-21, 2004,
Vol. 3119 of Springer Lecture Notes in Computer Science, 2004.
ISBN: 3-540-23029-7.
Copyright: Springer Verlag

[pdf]
2004-09-19-A: Predicate Logic with Sequence Variables and Sequence Function Symbols.
T. Kutsia, B. Buchberger
in A.Asperti, G.Bancerek, A.Trybulec (eds.): Proceedings of the Third International Conference on Mathematical Knowledge Management, MKM 2004, Bialowieza, POLAND, September 19-21, 2004,
Vol. 3119 of Springer Lecture Notes in Computer Science, 2004.
ISBN: 3-540-23029-7.
Copyright: Springer Verlag

[pdf]
2004-07-03-A: An Environment for Building Mathematical Knowledge Libraries
F. Piroi, B. Buchberger
in: Wolfgang Windsteiger, Christoph Benzmueller(eds), Proceedings of the Workshop on Computer-Supported Mathematical Theory Development, Second International Joint Conference (IJCAR) 2004, Cork, Ireland, July 4-8, 2004.



[pdf]
2004-04-09-A: Computational Origami: Interaction of Solving, Proving and Computing.
B. Buchberger, T. Ida
In: Proceedings of World Conference on 21st Century Mathematics, March 18 - 20, 2004, Lahore, Pakistan, accepted.



[nb]
2004-02-20-A: Towards the Automated Synthesis of a Groebner Bases Algorithm
B. Buchberger
RACSAM (Review of the Spanish Royal Academy of Science), submitted



[pdf]
2004-02-18-A: Algorithm Synthesis by Lazy Thinking: Examples and Implementation in Theorema.
B. Buchberger, A. Craciun.
Electronic Notes in Theoretical Computer Science, Vol. 93, 18 Feb. 2004, pp. 24-59, (Proc. of the Mathematical Knowledge Management Workshop, Edinburgh, Nov. 25, 2003, Fairouz Kamareddine ed.), http://www.sciencedirect.com/science/journal/15710661.
ISBN 044451290X


[pdf]
2003-10-04-B: Proving and Solving in Computational Origami
T.Ida, B. Buchberger
In: T.Jebelean, V.Negru, A.Popovici (eds.) Analele Universitatii din Timisoara, Seria Matematica - Informatica, vol. XLI, special issue on Computer Science - Proceedings of SYNASC'03 (International Workshop on Symbolic and Numeric Algorithms for Scientific Computing Timisoara, Romania, October 1 - 4, 2003), 2003, pg. 247-263.
ISSN 1224-970X
Copyright: Mirton Publisher, Timisoara, Romania

[pdf][ps][nb]
2003-10-04-A: Algorithm Invention and Verification by Lazy Thinking
B. Buchberger
In: T.Jebelean, V.Negru, A.Popovici (eds.) Analele Universitatii din Timisoara, Seria Matematica - Informatica, vol. XLI, special issue on Computer Science - Proceedings of SYNASC'03 (International Workshop on Symbolic and Numeric Algorithms for Scientific Computing Timisoara, Romania, October 1 - 4, 2003), 2003, pg. 41-70.
ISSN 1224-970X
Copyright: Mirton Publisher, Timisoara, Romania

[pdf]
2003-10-01-B: Algorithm Invention and Verification by Lazy Thinking
B. Buchberger
In: D. Petcu, V. Negru, D. Zaharie, T. Jebelean (eds.), Proceedings of SYNASC 2003, 5th International Workshop on Symbolic and Numeric Algorithms for Scientific Computing Timisoara, Romania, October 1 - 4, 2003, Mirton Publisher, pp. 2-26.
ISBN: 973-661-104-3
Copyright: Mirton Publisher, Timisoara, Romania

[nb]
2003-07-00-A: Solving Linear Boundary Value Problems Via Non–commutative Gröbner Bases
M. Rosenkranz,B. Buchberger, H. W. Engl
Applicable Analysis, Vol. 82, No. 7, July 2003, pp. 655-675.
ISSN 0003-6811, ISSN 1563-504X
Copyright: Taylor & Francis Ltd.

2003-00-00-A: Theorema: Computation and Deduction in Natural Style.
T. Jebelean, B. Buchberger
in: J. Grabmeier, E. Kaltofen, V. Weispfennig (eds.), Computer Algebra Handbook, Springer 2003, pp. 453 - 454.
ISBN 3-540-65466-6
Copyright: Springer - Verlag Berlin.

2002-12-19-A: Groebner Bases: The Commutative Case
B. Buchberger
In: A. V. Mikhalev, G. F. Pilz (eds), The Concise Handbook of Algebra, Kluwer Academic Publishers, 2002, pp. 262 – 265.
ISBN 0-7923-7072-4
Copyright: Kluwer Academic Publishers, Dordrecht, Netherlands.

2002-12-18-A: Groebner Bases: Applications
B. Buchberger
In: A. V. Mikhalev, G. F. Pilz (eds), The Concise Handbook of Algebra, Kluwer Academic Publishers, 2002, pp. 265-268.
ISBN 0-7923-7072-4
Copyright: Kluwer Academic Publishers, Dordrecht, Netherlands.

2002-10-09-B: Solving Linear Boundary Value Problems Via Non–commutative Gröbner Bases.
M. Rosenkranz,B. Buchberger, H. W. Engl
In: D. Petcu, V. Negru, D. Zaharie, T. Jebelean (eds.), Proceedings of SYNASC 2002, 4th International Workshop on Symbolic and Numeric Algorithms for Scientific Computing, Timisoara, Romania, October 9 -12, 2002, Mirton Publisher, pp. 300-313.
ISBN 973-585-785-5.
Copyright: Mirton Publisher, Timisoara, Romania

2002-10-09-A: Proving the Correctness of the Merge-Sort Algorithm with Theorema.
[AC], B. Buchberger
In: D. Petcu, V. Negru, D. Zaharie, T. Jebelean (eds.), Proceedings of SYNASC 2002, 4th International Workshop on Symbolic and Numeric Algorithms for Scientific Computing, Timisoara, Romania, October 9 -12, 2002, Mirton Publisher, pp. 97-111.
ISBN 973-585-785-5.
Copyright: Mirton Publisher, Timisoara, Romania

2001-12-00-A: Computers and Mathematical Research
B. Buchberger
In: C.Casacuberta, R. M. Miro-Roig, J. M. Ortega and S. Xambo-Descamps (eds.), Mathematical Glimpses into the 21st Century, Round Table at the Third European Congress of Mathematics, Barcelona, 2000, Artes Graficas Torres S.A., pp. 140-147.
ISBN: 84-89925-85-2
Copyright: Centro Internacional de Metodos Numericos en Ingenieria, Gran Capitan, Barcelona, Espana.

2001-10-02-A: Groebner Rings and Modules.
B. Buchberger
In: S. Maruster, B. Buchberger, V. Negru, T. Jebelean, Proceedings of SYNASC 2001 (The 3rd International Workshop on Symbolic and Numeric Algorithms for Scientific Computing), University of the West Timisoara, Romania, 2-5 October, 2001, pp.22-25.
RISC-Linz Report Series No. 01-20


Keywords: axiomatic approach to Groebner bases theory, least common reducibles
[abstract][ps][pdf]
2001-07-00-A: Groebner Bases and Systems Theory
B. Buchberger
Special Issue on "Applications of Groebner Bases in Multidimensional Systems and Signal Processing" (Z. Lin, L. Xu eds.) of the Journal "Multidimensional Systems and Signal Processing", Vol. 12, No. 3 / 4, October 2001, pp. 223-253.
ISSN 0923-6082
Copyright: Kluwer Academic Publishers, Boston.

2001-06-25-A: Logicographic Symbols: A New Feature in Theorema.
B. Buchberger
In: Y. Tazawa (ed.), Symbolic Computation - New Horizons (Proceedings of the 4th International Mathematica Symposium, Tokyo Denki University, Chiba New Town Campus, Japan, June 25-27, 2001), Tokyo Denki University Press, 2001, pp. 23-30.
ISBN 4-501-73020-X C3041
Copyright: Tokyo Denki University Press
Keywords: merge sort algorithm, relations and functions in set theory
[abstract][ps][pdf]
2001-06-18-A: Presenting Proofs Using Logicographic Symbols
K. Nakagawa,B. Buchberger
Proceedings of the Workshop on "Proof Transformation and Presentation" (A. Fiedler, H. Horacek eds.) at the IJAR-2001, Siena, June 18, 11 pages.


Keywords: Theorema, formal and intuitive representation, graphical semantics, Japanese Kanji system, Vedic literature, example merge sort, automated theorem proving
[abstract][ps][pdf]
2001-03-00-A: Theorema: A Proving System Based on Mathematica.
B. Buchberger
The Mathematica Journal, Vol. 8/2, pp. 247-252.
ISSN: 1047-5974
Copyright: Wolfram Research

2001-02-19-B: The PCS Prover in Theorema.
B. Buchberger
In: R. Moreno-Diaz, B. Buchberger, J.L. Freire (eds.), Proceedings of EUROCAST 2001 (8th International Conference on Computer Aided Systems Theory - Formal Methods and Tools for Computer Science), Feb. 19-23, 2001, Las Palmas de Gran Canaria, Lecture Notes in Computer Science 2178, 2201.
ISSN 0302-9743, ISBN 3-540-42959-X
Copyright: Springer - Verlag Berlin.
Keywords: proving - solving - computing, automated theorem proving, proof example, limit of sum, Collins' algorithm
[abstract][ps][pdf]
2001-02-19-A: Groebner Bases: A Short Introduction for Systems Theorists.
B. Buchberger
In: R. Moreno-Diaz, B. Buchberger, J.L. Freire (eds.), Proceedings of EUROCAST 2001 (8th International Conference on Computer Aided Systems Theory - Formal Methods and Tools for Computer Science), Feb. 19-23, 2001, Las Palmas de Gran Canaria, Lecture Notes in Computer Science 2178, 2201.
ISSN 0302-9743, ISBN 3-540-42959-X
Copyright: Springer - Verlag Berlin.
Keywords: motivation, intuition, definitions, theorems, examples, applications, complexity, history, references
[abstract][pdf]
2000-11-01-A: Computer-assisted Proving by the PCS Method.
B. Buchberger
Proceedings of the Workshop on Constructive Algebra, Amsterdam, Nov. 1-3, 2000, Springer Lecture Notes in Computer Science, submitted.


Keywords: automated theorem proving, Groebner bases, constructive and inconstructive proofs, theorem proving in analysis
[Appendix.pdf][abstract][pdf]
2000-10-06-A: Mathematics and Computer Science: A Personal View.
B. Buchberger
Analele Universitatii din Timisoara, Seria Matematica - Informatica, Vol. 38/1, 2000, pp.3-15.
ISSN 1224-970X


2000-10-04-A: Theory Exploration with Theorema
B. Buchberger
Analele Universitatii Din Timisoara, Ser. Matematica-Informatica, Vol. XXXVIII, Fasc.2, 2000, (Selected papers of SYNASC 2000, 2nd International Workshop on Symbolic and Numeric Algorithms in Scientific Computing, Oct. 4-6, 2000, Timisoara, Rumania, (T. Jebelean, V. Negru, A. Popovici eds.), pp. 9-32.
ISSN 1124-970X

Keywords: automated theorem proving, exploration situations, complete knowledge, bottom-up and top-down exploration, the proving cascade, transition from knowledge to inference rules, correctness of special inference rules
[abstract][ps][pdf]
2000-08-06-A: The Theorema Project: A Progress Report
B. Buchberger, C. Dupre, T. Jebelean, F. Kriftner, K. Nakagawa, D. Vasaru, W. Windsteiger
In: Symbolic Computation and Automated Reasoning (Proceedings of CALCULEMUS 2000, Symposium on the Integration of Symbolic Computation and Mechanized Reasoning, August 6-7, 2000, St. Andrews, Scotland), M. Kerber and M. Kohlhase (eds.), A.K. Peters, Natick, Massachusetts, pp. 98-113.
ISBN 1-56881-145-4.
Copyright: A.K. Peters, Natick, Massachusetts.
Keywords: Theorema formal text language, command language, computational sessions, PCS prover for predicate logic, semantic pattern matching, Groebner bases prover, Gosper-Zeilberger-Paule prover, meta-strategies, cascade, set theory prover
[abstract][ps][pdf]
2000-06-26-B: Theorem Proving For and With Gröbner Bases Theory
B. Buchberger
In: K. Galkowski (ed.), 2nd International Workshop on Multidimensional (nD) Systems, June 27-30, 2000, Csocha Castle, Lower Silesia, Poland, pp. 15-22.
ISBN: 83-85911-71-5
Copyright: Technical University Press, Zielona Gora, Poland

2000-05-22-A: Computer-Algebra: Das Ende der Mathematik? (Computer Algebra: The End of Mathematics?)
B. Buchberger
Mitteilungen der Deutschen Mathematiker-Vereinigung, Vol. 2, pp.16-19, 2000. (English Translation in: ACM SIGSAM Bulletin, March 2002. Danish Translation in: Matilde, Nr. 8, February 2000, pp. 4-7, Univ. of Kobenhavn.).
ISSN 0947-4471, ISSN: 1399-5901
Copyright: Birkhäuser Verlag AG, Basel, Switzerland.
Keywords: mathematical software systems, numerics, symbolics, automated theorem proving, trivialized mathematics, didactics of mathematics, purists, populists, sociology of mathematics, key technology of the information society, thinking technology, wavelets, Groebner bases, existence proofs, constructive proofs
[abstract][ps][pdf]
2000-03-00-A: Mathematik am Computer: Die nächste Überforderung? (Mathematics on the Computer: The Next Overtaxation?)
B. Buchberger
Didaktik-Reihe der Österreichischen Mathematischen Gesellschaft (Proceedings of a Symposium for High-school Teachers, September 24,1999, Graz, Austria), Vol.131, March 2000, pp. 37-56.



1999-00-00-A: Teaching of Mathematics Using Theorema.
B. Buchberger, T. Jebelean
The International Journal of Computer Algebra in Mathematical Education, Vol. 6, No. 1, pp. 25-50.
ISSN 1362-7368
Copyright: Research Information Ltd., UK.

1998-00-00-C: Theorema: A System for Formal Scientific Training in Natural Language Presentation.
B. Buchberger, T. Jebelean, D.Vasaru
Proceedings of Ed-Media 1998 (International Conference on Educational Multimedia), Freiburg, Germany, June 20-23, 1998, pp. 174-179.


1998-00-00-A: Introduction to Gröbner Bases
B. Buchberger
In: Gröbner Bases and Applications (B. Buchberger, F. Winkler, eds.), London Mathematical Society Lecture Notes Series 251, Cambridge University Press, 1998, pp.3-31.
ISBN 0-521-63298-6
[pdf]

1997-07-21-A: A Survey of the Theorema project.
B. Buchberger, T. Jebelean, F. Kriftner, M. Marin, E. Tomuta, D. Vasaru
In: Proceedings of ISSAC'97 (International Symposium on Symbolic and Algebraic Computation, Maui, Hawaii, July 21-23, 1997), W. Kuechlin (ed.), ACM Press 1997, pp. 384—391.
ISBN 0-89791-875-4


1997-00-00-D: Introduction to Groebner Bases.
B. Buchberger
In H.Schwichtenberg (ed.): Logic of Computation, NATO ASI Series, Series F: Computer and Systems Sciences, Vol. 157, Proceedings of the NATO Advanced Study Institute on Logic of Computation, Marktoberdorf, Germany, July 25-August 6, 1995, pp. 35-66.
ISBN 3-540-62963-7
Copyright: Springer - Verlag Berlin.

1997-00-00-C: Gröbner Bases
B. Buchberger
In: Encyclopaedia of Mathematics Supplement Volume I, (Editor-in-Chief: M. Hazewinkel), Kluwer Acad. Publ., 1997, pp. 275.



1997-00-00-B: Symbolic Computation (in German)
B. Buchberger
Chapter in: Handbuch der Informatik (G. Pomberger, P. Rechenberg eds.), Carl Hanser Verlag 2002, Munich, 1997, 1st edition, pp. 955-974; 3rd edition, pp. 963 – 981.



1997-00-00-A: Mathematica: Doing Mathematics by Computer?
B. Buchberger
In: A. Miola, M. Temperini (eds.), Advances in the Design of Symbolic Computation Systems, RISC Book Series on Symbolic Computation, Springer, Vienna, 1997, pp. 2-20.
ISSN 0943-853X, ISBN 3-211-82-844-3
Copyright: Springer, Wien.

1996-11-02-A: Using Mathematica for Doing Simple Mathematical Proofs.
B. Buchberger
Proceedings of the 4th Mathematica Users' Conference, Tokyo, November 2, 1996, Wolfram Media Publishing, pp. 80-96.



1996-11-01-A: Mathematica as a Rewrite Language.
B. Buchberger
In: T. Ida, A. Ohori, M. Takeichi (eds.), Functional and Logic Programming (Proceedings of the 2nd Fuji International Workshop on Functional and Logic Programming), November 1-4, 1996, Shonan Village Center), World Scientific, Singapore - New Jersey - London – Hong Kong, 1996, pp. 1-13.
ISBN 981-02-2923-2
Copyright: World Scientific, Singapore.
Keywords: design of Theorema, sequence variables, automated proving, automated induction, functors, syntax, algorithms and theorems
[abstract][ps][pdf]
1996-03-26-A: Symbolic Computation: Computer Algebra and Logic
B. Buchberger
In: F. Bader, K.U. Schulz (eds.) Frontiers of Combining Systems, Proceedings of FROCOS 1996 (1st International Workshop on Frontiers of Combining Systems), March 26-28, 1996, Munich, Applied Logic Series, Vol.3, Kluwer Academic Publisher, Dordrecht - Boston - London, 1996, pp. 193-220.

Copyright: Kluwer Academic Publishers, Dordrecht, Netherlands.
Keywords: design of Theorema, Mathematica, automated proving, automated induction, functors, syntax, algorithms and theorems
[abstract][ps][pdf]
1996-00-00-D: Mathematische Software-Systeme: Die Zukunft (Mathematical Software Systems: The Future)
B. Buchberger
Informatik-Spektrum, Vol. 19/2, 1996, Springer, Heidelberg, pp. 100--101



1996-00-00-C: Intelligent Systems Combining Reactive and Learning Capabilities
W. Jacak, B. Buchberger, S. Stifter
In: R. Trappl (ed.), Proceedings of the 13th European Meeting on Cybernetics and Systems Research, Vienna, Austria, 1996, Austrian Association for Cybernetic Studies, pp. 77-82.
ISBN 3 85206 133 4
Copyright: Austrian Society for Cybernetic Studies, Vienna.

1996-00-00-B: Intelligent Robotic Arm Based on Reactive Control
W. Jacak, B. Buchberger, S. Dreiseitl, T. Kubik
In: I. J. Rudas (ed.), Proceeding of the 5th International Workshop on Robotics in Alpe-Adria-Danube Region (RAAD'96), Budapest, Hungary, June 10-13, Hungarian Robotics Association, pp. 297-302.
ISBN 963 420 482 1
Copyright: Hungarian Robotics Association, Budapest.

1995-00-00-A: Symbolic Computation-Based Synthesis of Neural Network Dynamics and Controllers for Robots.
I. Duleba, W. Jacak, R. Muszynski, B. Buchberger
In: Proceedings of the 1995 IEEE International Conference on Neural Networks (ICNN'95), Perth, Australia, pp. 2720-2725, 1995.



1992-00-00-A: Using Gröbner Bases for Detecting Polynomial Identities. A Case Study on Fermat's Ideal
B. Buchberger, J. Elias
Journal of Number Theory, Vol. 41/3, pp. 272-279, July 1992, Academic Press 0022-314X/92.

Copyright: Academic Press, New York.

[pdf]
1991-09-23-A: Gröbner Bases in Mathematica: Enthusiasm and Frustration
B. Buchberger
In: P. W. Gaffney, E. N. Houstis (eds.), Proceedings of the IFIP Working Conference on Programming Environments for High-Level Symbolic Computation, September 23-27, Karlsruhe, Germany, Bergen Scientific Center Publishing, pp. 80-91, 1991.

Copyright: IBM, Bergen Scientific Center

[pdf]
1990-00-00-A: Should Students Learn Integration Rules?
B. Buchberger
ACM SIGSAM Bulletin Vol.24/1, pp. 10-17, January 1990.



[pdf]
1988-06-00-B: Algebraic Methods for Geometric Reasoning
B. Buchberger, G. E. Collins, B. Kutzler
Annual Reviews in Computer Science. Vol. 3, 1988, pp. 85-119.
8756-7016/88
Copyright: Annual Reviews Inc.

[pdf]
1987-04-00-A: History and Basic Features of the Critical-Pair/Completion Procedure
B. Buchberger
Journal of Symbolic Computation, Vol. 3, 1/2, 1987, pp. 3-38. (Earlier version appeared in: Proceedings of the Conference on Rewrite Technique and Applications, Dijon, May 1985, Lecture Notes in Computer Science, Vol. 202, Springer, 1985, pp. 1-45.)
ISSN 0747-7171
Copyright: Academic Press Inc., Harcourt Brace Jovanovich Publishers, London.

[pdf]
1987-03-00-A: Applications of Gröbner Bases in Non-Linear Computational Geometry.
B. Buchberger
IMA Volumes in Mathematics and its Applications, Vol. 14, Proceedings of the Workshop on Scientific Software, Minneapolis, USA, March 23-26, 1987, Springer, New York, pp. 59-88.

Copyright: Springer, New York

[paper.pdf][part1.pdf][part2.pdf]
1987-02-00-A: The Parallelization of Critical-Pair/Completion Procedures on the L-Machine.
B. Buchberger
Proc. of the Japanese Symp. on Functional Programming, Feb. 1987, RIKEN Institute, pp. 54-61.



1986-00-00-B: Computer-Algebra für den Ingenieur (Computer Algebra for the Engineer)
B. Buchberger, B. Kutzler
In: B. Buchberger, B. Kutzler, M. Feilmeier, M. Kratz, U. Kulisch, S. Rump (eds.): Rechnerorientierte Verfahren, Teubner Verlag, Stuttgart, 1986, pp. 11-68.
ISBN 3-519-02617-1
Copyright: Teubner, Stuttgart.

[part1.pdf][part2.pdf][paper.pdf]
1985-10-04-A: Mathematik für Informatiker: Ein algorithmenorientierte Ansatz an der Universität Linz (Mathematics for Computer Scientists: An Algorithm Oriented Approach at the University of Linz)
B. Buchberger
Proc. of the Mathematica Didactics Conference (R. Schaper ed.), Kassel, Oct. 4-6, 1984, Leuchtturm Verlag, 1985, pp. 156-172.



1985-09-00-A: The L-Language for the Parallel L-Machine (A Parallel Architecture for AI Applications)
B. Buchberger, P. Hintenaus
In: H. Trost, J. Retti (eds.), Proceedings of the Conference of the Austrian Society for Aritificial Intelligence, Vienna, September 1985, Informatik-Fachberichte, Vol. 106, pp. 120-131.
ISBN 3-540-15695-X
Copyright: Springer - Verlag Berlin.

[pdf]
1985-07-00-A: The L-Machine: An Attempt at Parallel Hardware for Symbolic Computation
B. Buchberger
Proceedings of the AAECC Conference, Grenoble, July 1985, Springer Lecture Notes in Computer Science 229, pp. 333-347.



[pdf]
1985-05-00-A: History and Basic Features of the Critical-Pair/Completion Approach.
B. Buchberger
In: Proceedings of the Conference on Rewrite Technique and Applications, Dijon, May 1985, Lecture Notes in Computer Science, Vol. 202, Springer, 1985, pp. 1-45.



1985-04-01-A: The Parallel L-Machine for Symbolic Computation
B. Buchberger
In B.F. Caviness (ed.): Proceedings of EUROCAL '85 (European Conference on Computer Algebra), Linz, Austria, April 1-3, 1985, Proceedings Vol.2: Research Contributions, Lectures Notes in Computer Science, Vol. 204, pp. 541-542.
ISBN 3-540-15984-3.
Copyright: Springer - Verlag Berlin.

[pdf]
1985-03-00-A: Algorithm 628: An Algorithm for Constructing Canonical Bases of Polynomial Ideals
F. Winkler, B. Buchberger, F. Lichtenberger, H. Rolletschek
ACM Transactions on Mathematical Software 11/1, March 1985, pp. 66-78



[pdf]
1985-00-00-B: Mathematik für Informatiker: Ein algorithmenorienter Ansatz an der Universität Linz (Mathematics for Computer Scientists: An Algorithm Oriented Approach at the University of Linz)
F. Lichtenberger, B. Buchberger
Zeitschrift für Hochschuldidaktik Vol. 9, No. 10, 1985, (Special issue: Proceedings of the Symposium "Lehr- und Lernprozesse in der Ingenieurausbildung", Technische Universität Graz, Austria, October 8-9, 1985), pp. 103-110.
ISBN 3-900386-10-2


[pdf]
1985-00-00-A: Gröbner-Bases: An Algorithmic Method in Polynomial Ideal Theory
B. Buchberger
Chapter 6 in: N.K. Bose (ed.), Multidimensional Systems Theory - Progress, Directions and Open Problems in Multidimensional Systems, Reidel Publishing Company, Dodrecht - Boston - Lancaster, 1985, pp. 184-232. (Second editioin: N.K.Bose (ed.): Multidimensional Systems Theory and Application, Kluwer Academic Publisher, 2003, pp.89-128.)
ISBN 90-277-1764-8, ISBN 1-4020-1623-9.
Copyright: Reidel Publishing Company, Dordrecht, Netherlands.

[part1.pdf][part2.pdf]
1984-12-00-A: Towards a Connection Machine for Logical Inference.
W. Bibel, B. Buchberger
Fifth Generation and Supercomputer Conference, Rotterdam, Dec. 1984. Appeared in Future Generation Computer Systems 1/3, 177-188.



[pdf]
1984-06-05-A: The Present State of the L-Networks Project
B. Buchberger
In: G. Mastronardi (ed.), Proceedings MIMI 84 (Conference on Mini- and Microcomputers and Their Applications), Bari, Juni 5-8, 1984, Acta Press, Anaheim - Calgary - Zurich, pp. 178-181.
ISBN 0-88986-058-0
Copyright: Acta Press, Anaheim.

[pdf]
1984-00-00-F: A Critical-Pair/Completion Algorithm for Finitely Generated Ideals in Rings.
B. Buchberger
In: E. Börger, G. Hasenjaeger, D. Rödding (eds), Logic and Machines: Decision Problems and Complexity (Proceedings of the Symposium "Rekursive Kombinatorik", Münster, May 23-28, 1983), Lecture Notes in Computer Science, Vol. 171, Springer, Berlin - Heidelberg - New York -Tokyo, 1984, pp. 137-161.
ISBN 3-540-13331-3, ISBN 0-387-13331-3
Copyright: Springer - Verlag Berlin.

[pdf]
1984-00-00-B: Automatisches Programmieren (Automated Programming)
B. Buchberger
In: J. Retti et al. (eds.) Artificial Intelligence - Eine Einführung, Teubner, Stuttgart, 1984, pp. 169-198.
ISBN 3-519-02473-X
Copyright: B.G.Teubner, Stuttgart.

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1983-09-00-A: A Criterion for Eliminating Unnecessary Reductions in the Knuth-Bendix Algorithm
F. Winkler, B. Buchberger
Colloquia Mathematica Societatis Janos Bolyai, Vol. 42, (Proceedings of Algebra and Logic in Computer Science, Györ, Hungary, Sept. 1983), pp. 849-869.



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1983-06-00-A: Components for Restructurable Multi-Microprocessor Systems of Arbitrary Topology
B. Buchberger
Prof. of the 21st Symp. on Mini- and Microcomputers, MIMI 83, Lugano, June 1983, pp. 67-71.



1983-03-28-A: A Note on the Complexity of Constructing Gröbner-Bases
B. Buchberger
In: J.A. van Hulzen (ed.), Computer Algebra (Proceedings of EUROCAL 83, European Computer Algebra Conference, London, March 28-30, 1983), Lecture Notes in Computer Science, Vol. 162, Springer Berlin - Heidelberg - New York - Tokyo, pp. 137-145.
ISBN 3-540-12868-9
Copyright: Springer - Verlag Berlin.

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1982-04-00-A: The Construction of Multivariate Polynomials with Pre-assigned Zeros
H. Möller, B. Buchberger
In: J. Calmet (ed.), Computer Algebra (Proceedings of EUROCAM '82, European Computer Algebra Conference), Marseille, April 5-7, 1982, Lecture Notes in Computer Science Vol. 144, Springer Berlin - Heidelberg - New York, 1982, pp. 24-31.
ISBN 3-540-11607-9
Copyright: Springer - Verlag Berlin.

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1982-03-15-A: Computer-unterstützter Algorithmenentwurf (Computer-Aided Algorithm Design)
B. Buchberger
In: W. Bibel, J. H. Siekmann (eds.), Proceedings of the Frühjahrsschule Künstliche Intelligenz, Teisendorf, March 15-24, 1982, Informatik-Fachberichte, Vol. 59, Springer -Verlag Berlin - Heidelberg - New York, 1982, pp. 141-202.
ISBN 3-540-11974-4
Copyright: Springer - Verlag Berlin.

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1982-00-00-B: Algebraic Simplification
B. Buchberger, R. Loos
In: B. Buchberger, G. E. Collins, R. Loos (eds.), Computer Algebra - Symbolic and Algebraic Computation, Springer Verlag, Vienna - New York, 1982, pp. 11-43.

Copyright: Springer Verlag, Vienna.

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1980-09-00-A: A Universal Variable-Topology Multi-Microcomputer-System
B. Buchberger, K. Aspetsberger
Proc. of the 6th International Symphosium on Mini- and Microcomputers, MIMI '80, Budapest, Hungary, September, 1980, pp. 136-140.



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1980-00-00-A: A Simplified Proof of the Characterization Theorem for Groebner-Bases
L. Bachmair, B. Buchberger
ACM SIGSAM Bull. 14/4, Novemer 1980, pp. 29-34.

Copyright: ACM, New York.

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1979-06-26-A: A Criterion for Detecting Unnecessary Reductions in the Construction of Gröbner Bases
B. Buchberger
In: E. W. Ng (ed.), Proceedings of the EUROSAM 79 Symposium on Symbolic and Algebraic Manipulation, Marseille, June 26-28, 1979, Lecture Notes in Computer Science, Vol. 72, Springer, Berlin - Heidelberg - New York, 1979, pp. 3-21.
ISBN 3-540-09519-5
Copyright: Springer - Verlag Berlin.

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1979-00-00-A: Computer Trees: A Concept for Parallel Processing
B. Buchberger, J. Fegerl, F. Lichtenberger
Microprocessing and Microsystems 3/6, 1979, pp. 244-248.



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1978-05-00-A: An Improved Algorithmic Construction of Gröbner Bases for Polynomial Ideals
C. Kollreider, B. Buchberger
ACM SIGSAM Bull. 12/2, May, 1978, pp. 27-36.



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1978-04-00-B: Systems with Universal Subsystems: Realization and Application
B. Buchberger, B. Quatember
Proc. of the Fourth European Meeting on Cybernetics and Systems Research, Linz, April 1978. Progress in Cybernetics and Systems Research, Vol. VII, Hemisphere Publ. Corp., 1978, pp. 25-32



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1978-02-00-A: Computer-Trees and Their Programming
B. Buchberger
Proc. of the 4th Coll. "Les arbres en algebre et en programmation", Feb.16-18, 1978, University of Lille, Dpt. of Computer Science, pp. 1-18, 1978.



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1978-00-00-B: Input/Output Codings and Transition Functions in Effective Systems.
B. Buchberger, B. Roider
Internat. Journal on General Systems 4/3, 201-209, 1978.



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1976-01-01-A: Das Problem der Programmverifikation (The Problem of Program Verification)
B. Buchberger
In: Jahrbuch Überblicke Mathematik 1976, Bibliographischs Institut, Mannheim, 1976, pp. 163-188, Bibliographisches Institut AG Zürich.
ISBN 3-411-01505-5
Copyright: Bibliographisches Institut AG Zürich.
Keywords: Sorting, example, inductive assertions
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1976-00-00-C: Some Properties of Gröbner Bases for Polynomial Ideals
B. Buchberger
ACM SIGSAM Bull. 10/4, 1976, pp. 19-24.

Copyright: ACM, New York.

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1976-00-00-A: A Theoretical Basis for the Reduction of Polynomials to Canonical Forms
B. Buchberger
ACM SIGSAM Bull. 10/3, 1976, pp. 19-29.

Copyright: ACM, New York.

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1974-08-07-A: Certain Decompositions of Gödel Numberings and the Semantics of Programming Languages
B. Buchberger
In: A. Ershov, V. A. Nepomniaschy (eds.), Proceedings of the International Symposium on Theoretical Programming, August 7-11, 1972, Novosibirsk, Lecture Notes in Computer Science, Vol. 5, Springer Berlin - Heidelberg - New York, 1974, pp. 152-171. (Appeared earlier in Russian in: Teoriya Programmirovaniya, part I., Trudy Simposiuma, Novosibirsk, 7-11 August, 1972, Ak. Nauk SSSR, Sibirian Division, Computing Center, pp. 250-266)
ISBN 3-540-067200-5
Copyright: Springer - Verlag Berlin.

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1974-00-00-A: On Certain Decompositions of Goedel Numberings
B. Buchberger
Archiv für math. Logik und Grundlagenforschung 16/1-2, 85-96, 1974.



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1973-05-00-A: Metody obratscheniya trechdiagonal'nyx matrits (Methods for the Inversion of Tridiagonal Matrices)
B. Buchberger, G.A. Yemel'yananko
Zhurnal vych. mat. i mat. fiziki Vol. 13/3, 1973, pp. 546-554. (English translation: USSR Computational Mathematics and Mathematical Physics, Vol. 13/3, 1973, pp. 10-20.)



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1972-00-00-A: Bemerkung zu den Reduzierbarkeitskriterien von R.Albrecht für das Optimum-Mix-Problem (A Comment on the Reducibility Criteria of R. Albrecht for the Optimum-Mix-Problem)
B. Buchberger
Zeitschrift für Operations Research 16, 1972, pp. 137-143, Physica-Verlag, Würzburg.



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1971-00-00-D: Metody obrashteniya trehdiagonal'nih matrits (appeared in russian; english title: Methods of Inverting Tridiagonal Matrices)
B. Buchberger, Emelyanenko G.A.
Communications of the Joint Institute for Nuclear Research (JINR), Dubna, No. P11-5686, 1971, 16 pages.



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1971-00-00-C: O Velichinah S(i) Opredelennih Rekursiej S(i+1)= u(i) . S(i) + v(i) . S(i-1). (On the Values S(i) Determined by the Recursion S(i+1)= u(i) . S(i) + v(i) . S(i-1).)
B. Buchberger
Communications of the Joint Institute for Nuclear Research (JINR), Dubna, No. P5-5789, 1971, 12 pages.



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1971-00-00-B: Associiruyushtshije Funksii i Operator Obyslovlennoj Iteratsii. (Associating Functions and the Operator of Conditioned Iteration.)
B. Buchberger
Communications of the Joint Institute for Nuclear Research (JINR), Dubna, No. P5-5788, 1971, 18 pages. (English Translation: Bericht Nr. 71-1, June 1971, 16 pages, Universität Innsbruck, Institut für Informatik.)



[abstract][english.pdf][pdf]
1971-00-00-A: An Extension of ALGOL 60
B. Buchberger
Communications of the Joint Institute for Nuclear Research (JINR), Dubna, No. E5-5787, 1971, 14 pages.



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1970-00-00-B: Algorithm 13: Lösung eines Optimum-Mix Problemes (Solution of an Optimum-Mix-Problem)
R. Albrecht, B. Buchberger
Computing 5, 1970, pp. 324-331.

Copyright: Springer Verlag

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1970-00-00-A: Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems (An Algorithmic Criterion for the Solvability of Algebraic Systems of Equations)
B. Buchberger
Aequationes mathematicae 4/3, 1970, pp. 374-383. (English translation in: B. Buchberger, F. Winkler (eds.), Gröbner Bases and Applications, Proceedings of the International Conference "33 Years of Groebner Bases", 1998, RISC, Austria, London Mathematical Society Lecture Note Series, Vol. 251, Cambridge University Press, 1998, pp. 535 -545.)

Copyright: Birkhäuser Verlag AG, Basel, Switzerland.

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