On span programs (1993)
| Venue: | In Proc. of the 8th IEEE Structure in Complexity Theory |
| Citations: | 106 - 5 self |
BibTeX
@INPROCEEDINGS{Karchmer93onspan,
author = {M. Karchmer and A. Wigderson},
title = {On span programs},
booktitle = {In Proc. of the 8th IEEE Structure in Complexity Theory},
year = {1993},
pages = {102--111},
publisher = {IEEE Computer Society Press}
}
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Abstract
We introduce a linear algebraic model of computation, the Span Program, and prove several upper and lower bounds on it. These results yield the following applications in complexity and cryptography: • SL ⊆ ⊕L (a weak Logspace analogue of N P ⊆ ⊕P). • The first super-linear size lower bounds on branching programs that count. • A broader class of functions which posses information-theoretic secret sharing schemes. The proof of the main connection, between span programs and counting branching programs, uses a variant of Razborov’s general approximation method. 1
