## On span programs (1993)

Venue: | In Proc. of the 8th IEEE Structure in Complexity Theory |

Citations: | 120 - 6 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}

}

### OpenURL

### 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