On arithmetic branching programs

A. Beimel; A. Gál

doi:10.1109/CCC.1998.694592

On arithmetic branching programs

A. Beimel, A. Gál

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

4 Scopus citations

Abstract

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.

Original language	English
Title of host publication	Proceedings - 13th Annual IEEE Conference on Computational Complexity, CCC 1998
Publisher	Institute of Electrical and Electronics Engineers
Pages	68-80
Number of pages	13
ISBN (Print)	0818683953
DOIs	https://doi.org/10.1109/CCC.1998.694592
State	Published - 1 Jan 1998
Externally published	Yes
Event	13th Annual IEEE Conference on Computational Complexity, CCC 1998 - Buffalo, United States Duration: 15 Jun 1998 → 18 Jun 1998

Publication series

Name	Proceedings of the Annual IEEE Conference on Computational Complexity
ISSN (Print)	1093-0159

Conference

Conference	13th Annual IEEE Conference on Computational Complexity, CCC 1998
Country/Territory	United States
City	Buffalo
Period	15/06/98 → 18/06/98

ASJC Scopus subject areas

Software
Theoretical Computer Science
Computational Mathematics

Access to Document

10.1109/CCC.1998.694592

Cite this

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title = "On arithmetic branching programs",

abstract = "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.",

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Beimel, A & Gál, A 1998, On arithmetic branching programs. in Proceedings - 13th Annual IEEE Conference on Computational Complexity, CCC 1998., 694592, Proceedings of the Annual IEEE Conference on Computational Complexity, Institute of Electrical and Electronics Engineers, pp. 68-80, 13th Annual IEEE Conference on Computational Complexity, CCC 1998, Buffalo, United States, 15/06/98. https://doi.org/10.1109/CCC.1998.694592

On arithmetic branching programs. / Beimel, A.; Gál, A.
Proceedings - 13th Annual IEEE Conference on Computational Complexity, CCC 1998. Institute of Electrical and Electronics Engineers, 1998. p. 68-80 694592 (Proceedings of the Annual IEEE Conference on Computational Complexity).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - On arithmetic branching programs

AU - Beimel, A.

AU - Gál, A.

PY - 1998/1/1

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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.

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M3 - Conference contribution

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T3 - Proceedings of the Annual IEEE Conference on Computational Complexity

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

PB - Institute of Electrical and Electronics Engineers

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ER -

On arithmetic branching programs

Abstract

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ASJC Scopus subject areas

Access to Document

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