TY - GEN

T1 - On arithmetic branching programs

AU - Beimel, A.

AU - Gál, A.

N1 - Funding Information:
Supported by grants ONR-M00014-96-1-0550 and ARO-DAAL03-92-G0115. Part of this work was done while the author was a postdoctoral fellow at DIMACS, supported in part by NSF under contract STC-91-19999 and the New Jersey Commission on Science and Technology. partially supported by ITRC, an Ontario Centre of Excellence. Part of this work was done while the author was a postdoctoral fellow at DIMACS and the Dept. of Computer Science of Princeton University, supported in part by NSF under contract STC-91-19999 and the New Jersey Commission on Science and Technology. We would like to thank Eric Allender, Allan Borodin, Eyal Kushilevitz, and Avi Wigderson for helpful discussions, and the anonymous referees for helpful comments.
Publisher Copyright:
© 1998 IEEE.

PY - 1998/1/1

Y1 - 1998/1/1

N2 - We consider the model of arithmetic branching programs, which is a generalization of modular branching programs. We show that, up to a polynomial factor in size, arithmetic branching programs are equivalent to complements of dependency programs. Using this equivalence we prove that dependency programs are closed under conjunction over every field. Furthermore, we show that span programs, an algebraic model of computation introduced by M. Karchmer and A. Wigderson (1993), are at least as strong as arithmetic programs; every arithmetic program can be simulated by a span program of size nod more than twice the size of the arithmetic program. Using the above results we give a new proof that NL/poly ⊆ ⊕ L/poly, first proved by A. Wigderson (1995). Our simulation of NL/poly is more efficient, and it holds for logspace counting classes over every field.

AB - We consider the model of arithmetic branching programs, which is a generalization of modular branching programs. We show that, up to a polynomial factor in size, arithmetic branching programs are equivalent to complements of dependency programs. Using this equivalence we prove that dependency programs are closed under conjunction over every field. Furthermore, we show that span programs, an algebraic model of computation introduced by M. Karchmer and A. Wigderson (1993), are at least as strong as arithmetic programs; every arithmetic program can be simulated by a span program of size nod more than twice the size of the arithmetic program. Using the above results we give a new proof that NL/poly ⊆ ⊕ L/poly, first proved by A. Wigderson (1995). Our simulation of NL/poly is more efficient, and it holds for logspace counting classes over every field.

UR - http://www.scopus.com/inward/record.url?scp=85031632064&partnerID=8YFLogxK

U2 - 10.1109/CCC.1998.694592

DO - 10.1109/CCC.1998.694592

M3 - Conference contribution

AN - SCOPUS:85031632064

SN - 0818683953

T3 - Proceedings of the Annual IEEE Conference on Computational Complexity

SP - 68

EP - 80

BT - Proceedings - 13th Annual IEEE Conference on Computational Complexity, CCC 1998

PB - Institute of Electrical and Electronics Engineers

T2 - 13th Annual IEEE Conference on Computational Complexity, CCC 1998

Y2 - 15 June 1998 through 18 June 1998

ER -