An upper bound on the space complexity of random formulae in resolution
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 36 (2002) no. 4, pp. 329-339.

We prove that, with high probability, the space complexity of refuting a random unsatisfiable Boolean formula in k-CNF on n variables and m=Δn clauses is On·Δ -1 k-2 .

DOI : 10.1051/ita:2003003
Classification : 68Q25, 03B05, 03F20
Mots clés : random formulae, space complexity, satisfiability threshold
@article{ITA_2002__36_4_329_0,
     author = {Zito, Michele},
     title = {An upper bound on the space complexity of random formulae in resolution},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {329--339},
     publisher = {EDP-Sciences},
     volume = {36},
     number = {4},
     year = {2002},
     doi = {10.1051/ita:2003003},
     mrnumber = {1965420},
     zbl = {1034.68050},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ita:2003003/}
}
TY  - JOUR
AU  - Zito, Michele
TI  - An upper bound on the space complexity of random formulae in resolution
JO  - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY  - 2002
SP  - 329
EP  - 339
VL  - 36
IS  - 4
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/ita:2003003/
DO  - 10.1051/ita:2003003
LA  - en
ID  - ITA_2002__36_4_329_0
ER  - 
%0 Journal Article
%A Zito, Michele
%T An upper bound on the space complexity of random formulae in resolution
%J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
%D 2002
%P 329-339
%V 36
%N 4
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/ita:2003003/
%R 10.1051/ita:2003003
%G en
%F ITA_2002__36_4_329_0
Zito, Michele. An upper bound on the space complexity of random formulae in resolution. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 36 (2002) no. 4, pp. 329-339. doi : 10.1051/ita:2003003. http://www.numdam.org/articles/10.1051/ita:2003003/

[1] D. Achlioptas and G.B. Sorkin, Optimal myopic algorithms for random 3-SAT, in 41st Annual Symposium on Foundations of Computer Science (2000) 590-600. | MR

[2] M. Alekhnovich, E. Ben-Sasson, A.A. Razborov and A. Wigderson, Space complexity in propositional calculus, in Proc. of the 32nd Annual ACM Symposium on Theory of Computing. Portland, OR (2000).

[3] P. Beame, R. Karp, T. Pitassi and M. Saks, On the complexity of unsatisfiability proofs for random k-CNF formulas, in Proc. of the 30th Annual ACM Symposium on Theory of Computing. New York (1998) 561-571. | MR | Zbl

[4] E. Ben-Sasson and N. Galesi, Space complexity of random formulae in resolution, in Proc. of the 16th Annual IEEE Conference on Computational Complexity. IEEE Computer Society (2001).

[5] B. Bollobás, C. Borgs, J.T. Chayes, J.H. Kim and D.B. Wilson, The scaling window of the 2-SAT transition. Random Structures Algorithms 18 (2001) 201-256. | MR | Zbl

[6] P. Cheeseman, B. Kanefsky and W.M. Taylor, Where the really hard problems are, in Proc. of IJCAI-91, edited by Kauffmann (1991) 331-337. | Zbl

[7] V. Chvátal and E. Szemerédi, Many hard examples for resolution. J. ACM 35 (1988) 759-768. | MR | Zbl

[8] S.A. Cook and R. Reckhow, The relative efficiency of propositional proof systems. J. Symb. Logic 44 (1979) 36-50. | MR | Zbl

[9] M. Davis, G. Logemann and D. Loveland, A machine program for theorem proving. Commun. ACM 5 (1962) 394-397. | MR | Zbl

[10] M. Davis and H. Putnam, A computing procedure for quantification theory. J. ACM 7 (1960) 201-215. | MR | Zbl

[11] J. Esteban and J.L. Toran, Space bounds for resolution, edited by C. Meinel and S. Tison, in STACS 99: 16th Annual Symposium on Theoretical Aspects of Computer Science, Trier, Germany, March 1999, Proceedings. Springer-Verlag, Lecture Notes in Comput. Sci. 1563 (1999) 551-560. | MR | Zbl

[12] A. Goerdt, A threshold for unsatisfiability. J. Comput. System Sci. 53 (1996) 469-486. | MR | Zbl

[13] T. Hagerup and C. Rüb, A guided tour of Chernoff bounds. Inform. Process. Lett. 33 (1989) 305-308. | MR | Zbl

[14] A.C. Kaporis, L.M. Kirousis, Y.C. Stamatiou, M. Vamvakari and M. Zito, Coupon collectors, q-binomial coefficients and the unsatisfiability threshold, edited by A. Restivo, S. Ronchi della Rocca and L. Roversi. Theoret. Comput. Sci., in 7th Italian Conference, ICTCS 2001. Springer-Verlag, Lecture Notes in Comput. Sci. 2202 (2001) 328-338. | MR | Zbl

[15] R. Bruce King, Beyond the quartic equation. Birkhauser, Boston, MA (1996). | MR | Zbl

[16] R. Bruce King and E. Rodney Canfield, An algorithm for calculating the roots of a general quintic equation from its coefficients. J. Math. Phys. 32 (1991) 823-825. | MR | Zbl

[17] I. Stewart, Galois Theory. Chapman and Hall, London (1973). | MR | Zbl

[18] J. Toran, Lower bounds for the space used in resolution, edited by J. Flum and M. Rodriguez-Artalejo, in Computer Science Logic: 13th International Workshop, CSL'99, 8th Annual Conference of the EACSL, Madrid, Spain, September 20-25, 1999, Proceedings. Springer-Verlag, Lecture Notes in Comput. Sci. 1683 (1999). | Zbl

[19] B.L. Van Der Wärden, Algebra. Frederick Ungar Publishing Co., New York (1970).

[20] R.C. Weast, Handbook of Tables for Mathematics. Cleveland: The Chemical Rubber Co. (1964). | MR | Zbl

Cité par Sources :