Abstract
In this paper, the possibility of fast algorithm is discussed for mechanical theorem proving, where the degeneracy condition are considered in designing of these algorithms. It is found that all of the methods depend seriously on some principles appearing in Wu’s Method. In other words, some principles in Wu’s Method are the instinctive properties in these new fast algorithms of theorem proving.
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Tarski A. A Decision Method for Elementary Algebra and Geometry. 2nd ed. Univ. California Press, 1951.
Loveland D. Automated theorem-proving: A quarter-century review. InAutomated Theorem Proving: After 25 Years, Bledsoe W (ed.), Contemporary Mathematics 29, 1983. American Mathematical Society, Providence, Rhode Island, pp. 1–46.
Ferrante J, Rackoff C W. The computational complexity of logical theories. Lecture Notes in Mathematics, 718, 1979, Springer-Verlag, New York.
Mayr E, Meyer A. The complexity of the word problems for commutative semigroups and polynomials ideals.Advance in Mathematics, 1982, 46: 305–329.
Wu W T. Basic Principles of Mechanical Theorem Proving in Geometries (part on Elementary Geometries), Beijing: Science Press, 1984 (in Chinese).
Gao X, Lin D. Wu’s Method and Its Application. InMathematical Models, Ye Q (ed), Human Science and Technique Press, 1998.
Buchberger B. Groebner Bases: An Algorithmic Method in Polynomial Ideal Theory. In Bose K (ed.)Multidimenstional Systems Theory, D. Reidel Publishing Co., 1985, pp. 184–232.
Collins G. Quantifier elimination for real closed fields by cylindrical algebraic decompisition. InProc. 2nd GI Conf., pp. 134–183.
Loos R, Weispfenning V. Applying linear quantifiers elimination.The Computer Journal, 1993, 36(5): 450–462, Special Issue on Computational Quantifier Elimination.
Weispfenning V. Quantifier elimination for real algebra-the quadratic case and beyond.AAECC, 1997, 8(2): 85–101.
Yang L, Zhang J, Hou X. The System of Nonlinear Algebraic Equations and Mechanical Theorem-Proving. Shanghai Science and Education Press, 1996.
Yap, C. Symbolic treatment of geometric degeneracies.J. Sym. Comp., 1990, 10: 349–370.
Seidernberg A. Constructions in algebra.Trans. Am. Math. Soc., 1974, 197: 273–313.
Kobayashi H, Moritsugu S, Hogan R. On radical zero-dimension ideals.J. Symbolic Computation, 1989, 8: 545–552.
Gao X, Chou S. On the parameterization of algebraic curves. Technical report, Department of Computer Science, The University of Texas, Austin Texas, 1991.
Gallo G, Mishra B. The complexity of resolvent resolved. InProceedings of the Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, 1994, pp. 280–289.
van der Waerden B. Abstract Algebra. Prinston Press, 1963.
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Supported by National Natural Science Foundation of China
LI Lian, born in November 1951, graduated from Dept. of Mathematics of Lanzhou University and got the M.S. degree in 1982. Now he is a Professor in Dept. of Compute Science of Lanzhou University.
Wang Jimin, born in October 1966, got the Master Degree in 1991. Now he is an Associate Professor in Dept. of Compute Science of Lanzhou University.
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Li, L., Wang, J. Fast theorem-proving and Wu’s Method. J. Comput. Sci. & Technol. 14, 481–486 (1999). https://doi.org/10.1007/BF02948789
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DOI: https://doi.org/10.1007/BF02948789