TY - JOUR
T1 - Boolean complexity classes vs. their arithmetic analogs
AU - Gál, Anna
AU - Wigderson, Avi
PY - 1996
Y1 - 1996
N2 - This paper provides logspace and small circuit depth analogs of the result of Valiant and Vazirani, which is a randomized (or nonuniform) reduction from NP to its arithmetic analog ⊕ P. We show a similar randomized reduction between the Boolean classes NL and semiunbounded fan-in Boolean circuits and their arithmetic counterparts. These reductions are based on the Isolation Lemma of Mulmuley, Vazirani, and Vazirani. Combinatorially our results can be viewed as simple (logspace) transformations of existential quantifiers into counting quantifiers in graphs and shallow circuits.
AB - This paper provides logspace and small circuit depth analogs of the result of Valiant and Vazirani, which is a randomized (or nonuniform) reduction from NP to its arithmetic analog ⊕ P. We show a similar randomized reduction between the Boolean classes NL and semiunbounded fan-in Boolean circuits and their arithmetic counterparts. These reductions are based on the Isolation Lemma of Mulmuley, Vazirani, and Vazirani. Combinatorially our results can be viewed as simple (logspace) transformations of existential quantifiers into counting quantifiers in graphs and shallow circuits.
UR - http://www.scopus.com/inward/record.url?scp=0040940655&partnerID=8YFLogxK
U2 - 10.1002/(SICI)1098-2418(199608/09)9:1/2<99::AID-RSA7>3.0.CO;2-6
DO - 10.1002/(SICI)1098-2418(199608/09)9:1/2<99::AID-RSA7>3.0.CO;2-6
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AN - SCOPUS:0040940655
SN - 1042-9832
VL - 9
SP - 99
EP - 111
JO - Random Structures and Algorithms
JF - Random Structures and Algorithms
IS - 1
ER -