@inproceedings{7b940dd3b45841d5b6e6a168634361fc,

title = "Computing algebraic formulas using a constant number of registers",

abstract = "We show that, over an arbitrary ring, the functions computed by polynomial-size algebraic formulas are also computed by polynomial-length algebraic straight-line programs which use only 3 registers (or 4 registers, depending on some definitions). We also show that polynomial-length products of 3×3 matrices compute precisely those functions that polynomial-size formulas compute (whereas, for general rings, polynomial-length 3-register straightline programs compute strictly more functions than polynomial-size formulas). This can be viewed as an extension of the results of Harrington in [Bal,Ba2] from the Boolean setting to the algebraic setting of an arbitrary ring.",

author = "Michael Ben-Or and Richard Cleve",

year = "1988",

doi = "10.1145/62212.62236",

language = "American English",

isbn = "0897912640",

series = "Proceedings of the Annual ACM Symposium on Theory of Computing",

publisher = "Association for Computing Machinery",

pages = "254--257",

booktitle = "Proceedings of the 20th Annual ACM Symposium on Theory of Computing, STOC 1988",

note = "20th Annual ACM Symposium on Theory of Computing, STOC 1988 ; Conference date: 02-05-1988 Through 04-05-1988",

}