Arithmetic Circuits: A Chasm at Depth Four, 2008 49th Annual IEEE Symposium on Foundations of Computer Science, pp.67-75, 2008. ,
DOI : 10.1109/FOCS.2008.32
Minimizing DNF Formulas and AC^0_d Circuits Given a Truth Table, 21st Annual IEEE Conference on Computational Complexity (CCC'06) ,
DOI : 10.1109/CCC.2006.27
Non-commutative arithmetic circuits: depth reduction and size lower bounds, Theoretical Computer Science, vol.209, issue.1-2, pp.47-86, 1998. ,
DOI : 10.1016/S0304-3975(97)00227-2
URL : http://doi.org/10.1016/s0304-3975(97)00227-2
On Arithmetic Branching Programs, Journal of Computer and System Sciences, vol.59, issue.2, pp.195-220, 1999. ,
DOI : 10.1006/jcss.1999.1648
An exponential lower bound for depth 3 arithmetic circuits, Proceedings of the thirtieth annual ACM symposium on Theory of computing , STOC '98, pp.577-582, 1998. ,
DOI : 10.1145/276698.276872
Exponential lower bounds for depth 3 arithmetic circuits in algebras of functions over finite fields, Applicable Algebra in Engineering, Communication and Computing, vol.6, issue.10, pp.465-487, 2000. ,
Fooling Parity Tests with Parity Gates, Proc. APPROX and RANDOM 2004, pp.381-392 ,
DOI : 10.1007/978-3-540-27821-4_34
Lower Bounds for Syntactically Multilinear Algebraic Branching Programs, Proc. MFCS, pp.407-418, 2008. ,
DOI : 10.1007/978-3-540-85238-4_33
Expressing a fraction of two determinants as a determinant, Proceedings of the twenty-first international symposium on Symbolic and algebraic computation, ISSAC '08, pp.141-146, 2008. ,
DOI : 10.1145/1390768.1390790
URL : https://hal.archives-ouvertes.fr/ensl-00232169
Shallow circuits with high-powered inputs Preprint: http://arxiv, Proc. Seoond Symposium on Innovations in Computer Science (ICS 2011), 2010. ,
Polynômes et coefficients, 2003. ,
Characterizing Valiant's algebraic complexity classes, Journal of Complexity, vol.24, issue.1, pp.16-38, 2006. ,
DOI : 10.1016/j.jco.2006.09.006
URL : http://doi.org/10.1016/j.jco.2006.09.006
Efficient parallel evaluation of straight-line code and arithmetic circuits, VLSI Algorithms and Architectures (Proc. Aegean Workshop on Computing), 1986. ,
Rudimentary predicates and Turing calculations, Soviet Mathematics Doklady, vol.11, issue.6, pp.1462-1465, 1970. ,
Lower bounds for non-commutative computation, Proceedings of the twenty-third annual ACM symposium on Theory of computing , STOC '91, pp.410-418, 1991. ,
DOI : 10.1145/103418.103462
Balancing Syntactically Multilinear Arithmetic Circuits, computational complexity, vol.17, issue.4, pp.515-535, 2008. ,
DOI : 10.1007/s00037-008-0254-0
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.126.1639
Lower Bounds and Separations for Constant Depth Multilinear Circuits, computational complexity, vol.18, issue.2, pp.171-207, 2009. ,
DOI : 10.1007/s00037-009-0270-8
of Carus mathematical monographs, Combinatorial Mathematics, vol.201, 1963. ,
Classes of arithmetic circuits capturing the complexity of computing the determinant, IEICE T. Inf. Syst, vol.75, issue.1, pp.116-124, 1992. ,
Graph-theoretic arguments in low-level complexity, In Mathematical Foundations of Computer Science Lecture Notes in Computer Science, vol.53, pp.162-176, 1977. ,
DOI : 10.1007/3-540-08353-7_135
Completeness classes in algebra, Proceedings of the eleventh annual ACM symposium on Theory of computing , STOC '79, pp.249-261, 1979. ,
DOI : 10.1145/800135.804419
Exponential lower bounds for restricted monotone circuits, Proceedings of the fifteenth annual ACM symposium on Theory of computing , STOC '83, pp.110-116, 1983. ,
DOI : 10.1145/800061.808739
Fast Parallel Computation of Polynomials Using Few Processors, SIAM Journal on Computing, vol.12, issue.4, pp.641-644, 1983. ,
DOI : 10.1137/0212043
A Survey of Lower Bounds for Satisfiability and Related Problems, Foundations and Trends?? in Theoretical Computer Science, vol.2, issue.3, pp.197-303, 2007. ,
DOI : 10.1561/0400000012
Properties that characterize LOGCFL, Journal of Computer and System Sciences, vol.43, issue.2, pp.380-404, 1991. ,
DOI : 10.1016/0022-0000(91)90020-6
URL : http://doi.org/10.1016/0022-0000(91)90020-6
On the Power of Small-Depth Computation, Foundations and Trends?? in Theoretical Computer Science, vol.5, issue.1, pp.1-72, 2009. ,
DOI : 10.1561/0400000033