New developments in the theory of Gröbner bases and applications to formal verification

Journal of Pure and Applied Algebra - Tập 213 - Trang 1612-1635 - 2009
Michael Brickenstein1, Alexander Dreyer2, Gert-Martin Greuel3, Markus Wedler3, Oliver Wienand3
1Mathematisches Forschungsinstitut Oberwolfach, Schwarzwaldstr. 9-11, 77709 Oberwolfach-Walke, Germany
2Fraunhofer Institute for Industrial Mathematics (ITWM), Fraunhofer-Platz 1, 67663 Kaiserslautern, Germany
3University of Kaiserslautern, Erwin-Schrödinger-Straße, 67653 Kaiserslautern, Germany

Tài liệu tham khảo

McMillan, 1993

Hachtel, 1996

Kunz, 2002, SAT and ATPG: Algorithms for Boolean decision problems, vol. 654, 309

O. Wienand, The Groebner basis of the ideal of vanishing polynomials, arXiv:0709.2978v1[math.AC]

O. Wienand, Ph.D Thesis, University of Kaiserslautern, Germany (2009) (in preparation)

Adams, 2003, An introduction to Gröbner bases

Greuel, 2002

Becker, 1993, Gröbner bases, a computational approach to commutative algebra, 10.1007/978-1-4612-0913-3

Agargün, 1999, Unique factorization rings with zero divisors, Comm. Algebra, 27, 1967, 10.1080/00927879908826543

Galovich, 1978, Unique factorization rings with zero-divisors, Math. Mag., 51, 276, 10.2307/2690246

Bouvier, 1974, Structure des anneaux a factorisation unique, Publ. Dep. Math. (Lyon), 11, 39

Fletcher, 1969, Unique factorization rings, Proc. Cambridge Phil. Soc., 65, 579, 10.1017/S0305004100003352

Zariski, 1979, vol. 28

Norton, 2002, Strong Gröbner bases for polynomials over a principal ideal ring, Bull. Austral. Math. Soc., 66, 145, 10.1017/S0004972700020165

M. Ghasemzadeh, A new algorithm for the quantified satisfiability problem, based on zero-suppressed binary decision diagrams and memorization, Ph.D. Thesis, University of Potsdam, Potsdam, Germany, Nov. 2005. http://opus.kobv.de/ubp/volltexte/2006/637/

Bérard, 1999

Bachmann, 1998, Monomial representations for Gröbner bases computations, 309

M. Brickenstein, A. Dreyer, PolyBoRi: A framework for Gröbner basis computations with boolean polynomials, Electronic Proceedings of Effective Methods in Algebraic Geometry MEGA 2007, 2007. http://www.ricam.oeaw.ac.at/mega2007/electronic/26.pdf

M. Brickenstein, Slimgb: Gröbner Bases with Slim Polynomials, in: Rhine Workshop on Computer Algebra, 2006, pp. 55–66, Proc. RWCA’06, Basel, March 2006

G.-M. Greuel, G. Pfister, H. Schönemann, SINGULAR 3.0, A Computer Algebra System for Polynomial Computations, Centre for Computer Algebra, University of Kaiserslautern, 2005. http://www.singular.uni-kl.de

Hungerbühler, 2006, A generalization of the smarandache function, integers, Electronic J. Combinatorial Number Theory, 6

F. Somenzi, CUDD: CU decision diagram package, University of Colorado at Boulder, release 2.4.1 (2005). URL http://vlsi.colorado.edu/~fabio/CUDD/

Rossum, 2006

W. Stein, SAGE Mathematics Software, The SAGEGroup (2007). http://www.sagemath.org

Collart, 1997, Converting bases with the Gröbner walk, J. Symbolic Comput., 24, 465, 10.1006/jsco.1996.0145

Hoos, 2000, SATLIB: An online resource for research on SAT, 283

Eén, 2003, An extensible SAT-solver, vol. 2919, 502