TY - JOUR

T1 - Time-space tradeoffs for branching programs

AU - Beame, Paul

AU - Jayram, T. S.

AU - Saks, Michael

N1 - Funding Information:
1A preliminary version of this paper appeared in ‘‘Proceedings of 39th annual IEEE Symposium on Foundations of Computer Science, November, 1999,’’ pp. 254–263. 2Research supported by NSF Grant CCR-9303017. 3This work was part of this author’s Ph.D. dissertation, completed at University of Washington and was supported by NSF Grant CCR-9303017. The author was formerly known as Jayram S. Thathachar. 4Research supported by NSF Grant CCR-9700239. This work was done in part while on sabbatical at University of Washington.

PY - 2001/12

Y1 - 2001/12

N2 - We obtain the first non-trivial time-space tradeoff lower bound for functions f:{0,1}n → {0,1} on general branching programs by exhibiting a Boolean function f that requires exponential size to be computed by any branching program of length (1 + ε) n, for some constant ε > 0. We also give the first separation result between the syntactic and semantic read-k models (A. Borodin et al., Comput. Complexity 3 (1993), 1-18) for k > 1 by showing that polynomial-size semantic read-twice branching programs can compute functions that require exponential size on any semantic read-k branching program. We also show a time-space tradeoff result on the more general R-way branching program model (Borodin et al., 1993): for any k, we give a function that requires exponential size to be computed by length kn q-way branching programs, for some q = q(k). This result gives a similar tradeoff for RAMs, and thus provides the first nontrivial time-space tradeoff for decision problems in this model.

AB - We obtain the first non-trivial time-space tradeoff lower bound for functions f:{0,1}n → {0,1} on general branching programs by exhibiting a Boolean function f that requires exponential size to be computed by any branching program of length (1 + ε) n, for some constant ε > 0. We also give the first separation result between the syntactic and semantic read-k models (A. Borodin et al., Comput. Complexity 3 (1993), 1-18) for k > 1 by showing that polynomial-size semantic read-twice branching programs can compute functions that require exponential size on any semantic read-k branching program. We also show a time-space tradeoff result on the more general R-way branching program model (Borodin et al., 1993): for any k, we give a function that requires exponential size to be computed by length kn q-way branching programs, for some q = q(k). This result gives a similar tradeoff for RAMs, and thus provides the first nontrivial time-space tradeoff for decision problems in this model.

UR - http://www.scopus.com/inward/record.url?scp=0035733585&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035733585&partnerID=8YFLogxK

U2 - 10.1006/jcss.2001.1778

DO - 10.1006/jcss.2001.1778

M3 - Article

AN - SCOPUS:0035733585

SN - 0022-0000

VL - 63

SP - 542

EP - 572

JO - Journal of Computer and System Sciences

JF - Journal of Computer and System Sciences

IS - 4

ER -