Elimination of parameters in the polynomial hierarchy

Theoretical Computer Science

Volumn 215, Issue 1-2, 1999, Pages 289-304

  Koiran, Pascal ^a  

^a UNIV LYON   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0346207636     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(98)00261-8     Document Type: Article

References (20)

1. L. Babai, S. Moran, Arthur-Merlin games, A randomized proof system, and a hierarchy of complexity classes, J. Comput. System Sci. 36 (1988) 254-276.
2. J.L. Balcázar, J. Díaz, J. Gabarró, Structural Complexity I, EATCS Monographs on Theoretical Computer Science, Springer, Berlin, 1988.
3. L. Blum, F. Cucker, M. Shub, S. Smale, Algebraic settings for the problem "P≠NP?", in: J. Renegar, M. Shub, S. Smale (Eds.), The Mathematics of Numerical Analysis, Lectures in Applied Mathematics, vol. 32, American Mathematical Society, Providence, RI, 1996. pp. 125-144.
4. L. Blum, F. Cucker, M. Shub, S. Smale, Complexity and Real Computation, Springer, Berlin, 1998.
5. N. Bourbaki, Algèbre (Chapitres 4 à 7), Masson, Paris, 1981.
6. O. Chapuis, P. Koiran, Saturation and stability in the theory of computation over the reals, Ann. Pure Appl. Logic, to appear.
7. F. Cucker, M. Karpinski, P. Koiran, T. Lickteig, K. Werther, On real Turing machines that toss coins, in: Proc. 27th ACM Symp. on Theory of Computing, 1995, pp. 335-342.
8. N. Fichtas, A. Galligo, J. Morgenstern, Precise sequential and parallel complexity bounds for quantifier elimination over algebraically closed fields, J. Pure Appl. Algebra 67 (1990) 1-14.
9. J. Heintz, C.-P. Schnorr, Testing polynomials which are easy to compute, in: Logic and Algorithmic (an Internat. Symp. held in honour of Ernst Specker), pp. 237-254. Monographie no 30 de L'Enseignement Mathématique, 1982. Preliminary version in Proc. 12th ACM Symp. on Theory of Computing, 1980, pp. 262-272.
10. J. Heintz, C.-P. Schnorr, Testing polynomials which are easy to compute, in: Logic and Algorithmic (an Internat. Symp. held in honour of Ernst Specker), pp. 237-254. Monographie no 30 de L'Enseignement Mathématique, 1982. Preliminary version in Proc. 12th ACM Symp. on Theory of Computing, 1980, pp. 262-272.
11. S. Ivanov, M. de Rougemont, Interactive protocols on the reals, in: Proc. 15th Annu. Symp. on Theoretical Aspects of Computer Science, Lecture Notes in Computer Science, vol. 1373, Springer, Berlin, 1998, pp. 499-510.
12. P. Koiran, Approximating the volume of definable sets, in: Proc. 36th IEEE Symp. on Foundations of Computer Science, 1995, pp. 134-141.
13. P. Koiran, Hilbert's Nullstellensatz is in the polynomial hierarchy, J. Complexity 12 (4) (1996) 273-286. Long version: DIMACS report 96-27.
14. P. Koiran, Hilbert's Nullstellensatz is in the polynomial hierarchy, J. Complexity 12 (4) (1996) 273-286. Long version: DIMACS report 96-27.
15. P. Koiran, Elimination of constants from machines over algebraically closed fields, J. Complexity 13 (1) (1997) 65-82. Erratum on http://www.ens-lyon.fr/~koiran.
16. P. Koiran, Randomized and deterministic algorithms for the dimension of algebraic varieties, in: Proc. 38th IEEE Symp. on Foundations of Computer Science, 1997, pp. 36-45.
17. ℝ-complete, LIP Research Report 97-36, Ecole Normale Supérieure de Lyon, 1997.
18. B. Poizat, Groupes Stables, Nur Al-Mantiq Wal-Ma'rifah 2, 1987.
19. B. Poizat, Les Petits Cailloux, Nur Al-Mantiq Wal-Ma'rifah 3, Aléas, Lyon, 1995.
20. J.T. Schwarz, Fast probabilistic algorithms for verification of polynomials identities, J. ACM 27 (1980) 701-717.