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

Journal of Pure and Applied Algebra

Volumn 213, Issue 8, 2009, Pages 1612-1635

  Brickenstein, Michael ^a   Dreyer, Alexander ^b   Greuel, Gert Martin ^c   Wedler, Markus ^c   Wienand, Oliver ^c  

^a Mathematisches Forschungsinstitut Oberwolfach   (Germany)

^b FRAUNHOFER INSTITUTE FOR INDUSTRIAL MATHEMATICS ITWM   (Germany)

^c Rheinland Pfälzische Technische Universität Kaiserslautern Landau   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 63149098699     PISSN: 00224049     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jpaa.2008.11.043     Document Type: Article

References (32)

1. McMillan K.L. Symbolic Model Checking (1993), Kluwer Academic Publishers, Norwell, MA, USA
2. Hachtel G.D., and Somenzi F. Logic Synthesis and Verification Algorithms (1996), Kluwer Academic
3. Kunz W., Marques-Silva J., and Malik S. SAT and ATPG: Algorithms for Boolean decision problems. In: Hassoun S., and Sasao T. (Eds). Logic Synthesis and Verification. The Springer International Series in Engineering and Computer Science vol. 654 (2002), Kluwer Academic Publishers, Norwell, MA, USA 309-341
4. Smith D.J. VHDL & Verilog compared & contrasted-Plus modeled example written in VHDL, Verilog and C. DAC '96: Proceedings of the 33rd Annual Conference on Design Automation (1996), ACM Press, New York, NY, USA 771-776
5. O. Wienand, The Groebner basis of the ideal of vanishing polynomials, arXiv:0709.2978v1[math.AC]
6. O. Wienand, Ph.D Thesis, University of Kaiserslautern, Germany (2009) (in preparation)
7. Adams W., and Loustaunau P. An introduction to Gröbner bases. Graduate Studies in Mathematics (2003), AMS
8. Kalkbrener M. Algorithmic properties of polynomial rings. J. Symbolic Comput. 26 5 (1998) 525-581
9. Greuel G.-M., and Pfister G. A Singular Introduction to Commutative Algebra (2002), Springer
10. Becker T., and Weispfennig V. Gröbner bases, a computational approach to commutative algebra. Graduate Texts in Mathematics (1993), Springer Verlag
11. Agargün A.G. Unique factorization rings with zero divisors. Comm. Algebra 27 4 (1999) 1967-1974
12. Galovich S. Unique factorization rings with zero-divisors. Math. Mag. 51 (1978) 276-283
13. Bouvier A. Structure des anneaux a factorisation unique. Publ. Dep. Math. (Lyon) 11 (1974) 39-49
14. Fletcher C.R. Unique factorization rings. Proc. Cambridge Phil. Soc. 65 3 (1969) 579-583
15. Zariski O., and Samuel P. Commutative Algebra, Vol. I. Graduate Texts in Mathematics vol. 28 (1979), Springer
16. Norton G.H., and Salagean A. Strong Gröbner bases for polynomials over a principal ideal ring. Bull. Austral. Math. Soc. 66 (2002) 145-152
17. 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/
18. Bérard B., Bidoit M., Laroussine F., Petit A., Petrucci L., Schoenebelen P., and McKenzie P. Systems and Software Verification: Model-checking Techniques and Tools (1999), Springer-Verlag New York, Inc., New York, NY, USA
19. S. Minato, Implicit manipulation of polynomials using zero-suppressed BDDs, in: Proc. of IEEE The European Design and Test Conference, ED&TC'95, 1995, pp. 449-454
20. Bachmann O., and Schönemann H. Monomial representations for Gröbner bases computations. Proc. of the International Symposium on Symbolic and Algebraic Computation. ISSAC'98 (1998), ACM Press 309-316
21. 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
22. M. Brickenstein, Slimgb: Gröbner Bases with Slim Polynomials, in: Rhine Workshop on Computer Algebra, 2006, pp. 55-66, Proc. RWCA'06, Basel, March 2006
23. Giovini A., Mora T., Niesi G., Robbiano L., and Traverso C. One sugar cube, please or Selection strategies in Buchberger algorithms. In: Watt S. (Ed). Proceedings of the 1991 International Symposium on Symbolic and Algebraic Computations. ISSAC'91 (1991), ACM Press 49-54
24. 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
25. Hungerbühler N., and Specker E. A generalization of the smarandache function, integers. Electronic J. Combinatorial Number Theory 6 (2006) #A23
26. F. Somenzi, CUDD: CU decision diagram package, University of Colorado at Boulder, release 2.4.1 (2005). URL http://vlsi.colorado.edu/~fabio/CUDD/
27. A.A. Stepanov, M. Lee, The Standard Template Library, Tech. Rep. X3J16/94-0095, WG21/N0482, 1994
28. Rossum G.V., and Drake F.L. The Python Language Reference Manual (2006), Network Theory Ltd, Bristol, United Kingdom
29. W. Stein, SAGE Mathematics Software, The SAGEGroup (2007). http://www.sagemath.org
30. Collart S., Kalkbrener M., and Mall D. Converting bases with the Gröbner walk. J. Symbolic Comput. 24 (1997) 465-469
31. Hoos H.H., and Stützle T. SATLIB: An online resource for research on SAT. In: Gent I.P., Maaren H.v., and Walsh T. (Eds). SAT 2000 (2000), IOS Press 283-292
32. Eén N., and Sörensson N. An extensible SAT-solver. In: Giunchiglia E., and Tacchella A. (Eds). SAT. Lecture Notes in Computer Science vol. 2919 (2003), Springer 502-518. http://www.cs.chalmers.se/Cs/Research/FormalMethods/MiniSat/