Exponential Lower Bounds for Monotone Span Programs

2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS) ◽

10.1109/focs.2016.51 ◽

2016 ◽

Cited By ~ 16

Author(s):

Robert Robere ◽

Toniann Pitassi ◽

Benjamin Rossman ◽

Stephen A. Cook

Keyword(s):

Lower Bounds ◽

Monotone Span Programs ◽

Span Programs

Lower bounds for monotone span programs

Proceedings of IEEE 36th Annual Foundations of Computer Science ◽

10.1109/sfcs.1995.492669 ◽

1995 ◽

Cited By ~ 8

Author(s):

A. Beimel ◽

A. Gal ◽

M. Paterson

Keyword(s):

Lower Bounds ◽

Monotone Span Programs ◽

Span Programs

Lower Bounds for Monotone Span Programs

BRICS Report Series ◽

10.7146/brics.v1i46.21596 ◽

1994 ◽

Vol 1 (46) ◽

Cited By ~ 1

Author(s):

Amos Beimel

Keyword(s):

Lower Bounds ◽

Secret Sharing ◽

Algebraic Model ◽

New Technique ◽

Secret Sharing Schemes ◽

Branching Programs ◽

Model Of Computation ◽

Monotone Span Programs ◽

Span Programs ◽

A New Technique

The model of span programs is a linear algebraic model of computation. Lower bounds for span programs imply lower bounds for contact schemes, symmetric branching programs and for formula size. Monotone span programs correspond also to linear secret-sharing schemes. We present a new technique for proving lower bounds for monotone span programs. The main result proved here yields quadratic lower bounds for the size of monotone span programs, improving on the largest previously known bounds for explicit functions. The bound is asymptotically tight for the function corresponding to a class of 4-cliques.

A characterization of span program size and improved lower bounds for monotone span programs

Computational Complexity ◽

10.1007/s000370100001 ◽

2001 ◽

Vol 10 (4) ◽

pp. 277-296 ◽

Cited By ~ 23

Author(s):

Ana G�l

Keyword(s):

Lower Bounds ◽

Monotone Span Programs ◽

Span Programs

Extremal bipartite graphs and superpolynomial lower bounds for monotone span programs

Proceedings of the twenty-eighth annual ACM symposium on Theory of computing - STOC '96 ◽

10.1145/237814.238010 ◽

1996 ◽

Cited By ~ 9

Author(s):

László Babai ◽

Anna Gál ◽

János Kollár ◽

Lajos Rónyai ◽

Tibor Szabó ◽

...

Keyword(s):

Lower Bounds ◽

Bipartite Graphs ◽

Monotone Span Programs ◽

Span Programs

Superpolynomial Lower Bounds for Monotone Span Programs

COMBINATORICA ◽

10.1007/s004930050058 ◽

1999 ◽

Vol 19 (3) ◽

pp. 301-319 ◽

Cited By ~ 39

Author(s):

László Babai ◽

Anna Gál ◽

Avi Wigderson

Keyword(s):

Lower Bounds ◽

Monotone Span Programs ◽

Span Programs

A characterization of span program size and improved lower bounds for monotone span programs

Proceedings of the thirtieth annual ACM symposium on Theory of computing - STOC '98 ◽

10.1145/276698.276855 ◽

1998 ◽

Cited By ~ 10

Author(s):

Anna Gál

Keyword(s):

Lower Bounds ◽

Monotone Span Programs ◽

Span Programs

Lower bounds for monotone span programs

Computational Complexity ◽

10.1007/bf01202040 ◽

1996 ◽

Vol 6 (1) ◽

pp. 29-45 ◽

Cited By ~ 31

Author(s):

Amos Beimel ◽

Anna G�l ◽

Mike Paterson

Keyword(s):

Lower Bounds ◽

Monotone Span Programs ◽

Span Programs

On the Size of Monotone Span Programs

Security in Communication Networks - Lecture Notes in Computer Science ◽

10.1007/978-3-540-30598-9_18 ◽

2005 ◽

pp. 249-262 ◽

Cited By ~ 6

Author(s):

Ventzislav Nikov ◽

Svetla Nikova ◽

Bart Preneel

Keyword(s):

Monotone Span Programs ◽

Span Programs

Separating the Power of Monotone Span Programs over Different Fields

SIAM Journal on Computing ◽

10.1137/s0097539704444038 ◽

2005 ◽

Vol 34 (5) ◽

pp. 1196-1215 ◽

Cited By ~ 15

Author(s):

Amos Beimel ◽

Enav Weinreb

Keyword(s):

Monotone Span Programs ◽

Span Programs

Separating the power of monotone span programs over different fields

44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings. ◽

10.1109/sfcs.2003.1238216 ◽

2004 ◽

Cited By ~ 3

Author(s):

A. Beimel ◽

E. Weinreb

Keyword(s):

Monotone Span Programs ◽

Span Programs