H. Hong. Comparison of several decision algorithm for the existentional theory of the reals, 1991.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....arithmetic operations and size of output. From Grigoriev and Vorobjov s paper [16] new algorithms appeared, based on the critical point method. These algorithms have a single exponential complexity in the number of variables, in terms of basic arithmetic operations and size of output. Still, in [20], Hong shows that the algorithms proposed in the papers [24] and [16] are not usable in practice. According to the experiments in [31] the same conclusions apply for more recent methods like in [9, 30, 19] These algorithms adopt strategies of the following kind: In the rst place, solve the ....

....a real algebraic set de ned by a polynomial system, in the spirit of [10, 13] The experiments in [28, 6] show that these strategies are competitive with the CAD on small examples and allow to deal with more signi cant ones, unreachable with the CAD. In this paper, we pursue the investigations of [20] by analyzing the practical behavior of these two recent algorithms on the Birkho Interpolation Problem. In sections 3, 4 and 5, we recall the algorithm given in [28] our contribution being a new way to solve a system with in nitesimal parameters arising in its course, then the algorithm given ....

H. Hong, Comparison of Several Decision Algorithms for the Existential Theory of the Reals, Research report, RISC, 1991.

....of basic arithmetic operations and size of output. From Grigoriev and Vorobjov s paper [16] new algorithms appeared, based on the critical point method. These algorithms have a single exponential complexity in the number of variables, in terms of basic arithmetic operations and size of output. In [20], Hong shows that the algorithms proposed in the papers [24] and [16] are not usable in practice. According to the experiments in [31] the same conclusions apply for more recent methods like in [9, 30, 19] These algorithms adopt strategies of the following kind: In the rst place, solve the ....

....a real algebraic set de ned by a polynomial system, in the spirit of [10, 13] The experiments in [28, 6] show that these strategies are competitive with the CAD on small examples and allow to deal with more signi cant ones, unreachable with the CAD. In this paper, we pursue the investigations of [20] by analyzing the practical behavior of these two recent algorithms on the Birkho Interpolation Problem. In sections 3, 4 and 5, we recall the algorithm given in [28] our contribution being a new way to solve a system with in nitesimal parameters arising in its course, then the algorithm given ....

H. Hong, Comparison of Several Decision Algorithms for the Existential Theory of the Reals, Research report, RISC, 1991.

....domains enhances declarativeness. Solving systems of constraints over the reals is a very difficult task and a lot of work has still to be done in order to attain efficiency. The number of free variables is a critical measure of the complexity of deciding the polynomial system of equations [11] and therefore, it should be minimized. One examples are the variables generated by the renaming mechanism because they do not occur, in general, in the set of already solved constraints as remarked in [17] This suggests that one could try to eliminate them without resorting to the expensive ....

H. Hong. Comparison of Several Decision Algorithms for the Existential Theory of the Reals. Technical Report 91--41.0, Research Institute for Symbolic Computation, Johannes Kepler University A-4040 Linz, Austria, 1991. Submitted to Journal of Symbolic Computation.

.... through various improvements [11, 129, 92, 93, 123, 94, 48, 119, 28, 114] enabling mechanical solution of diverse nontrivial problems [13, 94, 95] Very recently several other methods with better theoretical complexities are proposed in the literature [78, 77, 143, 144] However the study by Hong [96] suggests that CAD is still the best one for practical purpose. ffl Grobner Basis, Characteristic Sets: These methods respectively by Buchberger [25] and Wu [168] solves, among many others, the following problem: Technical Annex PE7195 ACCLAIM 23 Given a system of polynomial equations with ....

....algebra. During last three decades three most promising methods have emerged: Cylindrical Algebraic Decomposition [47] Grobner basis [25] and Characteristic sets [168] The method of cylindrical algebraic decomposition was introduced by Collins [47] and has been significantly improved by Hong [92, 93, 94, 48, 49, 50, 28, 95, 96, 97, 101, 99, 100, 98]. This method solves, among many others, constraint satisfaction problems over the reals. Since its introduction, this method inspired intense research in algebraic methods for computational logic and real algebraic geometry, producing over 200 articles in the literature [12] The method of ....

H. Hong. Comparison of several decision algorithms for the existential theory of the reals. Technical Report 91--41.0, Research Institute for Symbolic Computation, Johannes Kepler University A-4040 Linz, Austria, 1991. Submitted to Journal of Symbolic Computation.

....theorem proving and discovery, termination proof of term rewrite systems, constraint solving in logic programming, etc. During 1930 1950, Tarski [34] found the first quantifier elimination algorithm in this theory. Since then various improvements and new methods have been devised and analyzed [33, 8, 17, 5, 9, 1, 28, 2, 4, 13, 15, 14, 7, 16, 29, 30, 31, 18, 19, 26, 20, 11, 25, 6, 23, 22]. In this paper we investigate the parallelization of the algorithm which was originally devised by Collins [9] and improved by the author [20] In [32] Saunders, Lee, and Abdali report their work on parallelizing Collins original algorithm on a shared memory machine, achieving about 50 ....

H. Hong. Comparison of several decision algorithms for the existential theory of the reals. Technical Report 91--41.0, Research Institute for Symbolic Computation, Johannes Kepler University A-4040 Linz, Austria, 1991.

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H. Hong. Comparison of several decision algorithm for the existentional theory of the reals, 1991.

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H. Hong. Comparison of several decision algorithm for the existentional theory of the reals, 1991.

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