On Span Programs

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 NP ⊆ ⊕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.

• Type: Conference
• Year: 1993
• Where: COCO
• Authors: Mauricio Karchmer, Avi Wigderson
• Keywords: Algorithms, Branching Programs, COCO 1993, Lower Bounds, Span Programs