Iwama, Kazuo ;
Nagao, Atsuki
ReadOnce Branching Programs for Tree Evaluation Problems
Abstract
Toward the ultimate goal of separating L and P, Cook, McKenzie, Wehr, Braverman and Santhanam introduced the tree evaluation problem (TEP). For fixed h, k>0, FT_h(k) is given as a complete, rooted binary tree of height h, in which each internal node is associated with a function from [k]^2 to [k], and each leaf node with a number in [k]. The value of an internal node v is defined naturally, i.e., if it has a function f and the values of its two child nodes are a and b, then the value of v is f(a,b). Our task is to compute the value of the root node by sequentially executing this function evaluation in a bottomup fashion. The problem is obviously in P and if we could prove that any branching program solving FT_h(k) needs at least k^(r(h)) states for any unbounded function r, then this problem is not in L, thus achieving our goal. The above authors introduced a restriction called thrifty against the structure of BP’s (i,e., against the algorithm for solving the problem) and proved that any thrifty BP needs Omega(k^h) states. This paper proves a similar lower bound for readonce branching programs, which allows us to get rid of the restriction on the order of nodes read by the BP that is the nature of the thrifty restriction.
BibTeX  Entry
@InProceedings{iwama_et_al:LIPIcs:2014:4475,
author = {Kazuo Iwama and Atsuki Nagao},
title = {{ReadOnce Branching Programs for Tree Evaluation Problems}},
booktitle = {31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)},
pages = {409420},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783939897651},
ISSN = {18688969},
year = {2014},
volume = {25},
editor = {Ernst W. Mayr and Natacha Portier},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2014/4475},
URN = {urn:nbn:de:0030drops44756},
doi = {10.4230/LIPIcs.STACS.2014.409},
annote = {Keywords: Lower bounds, Branching Programs, ReadOnce Branching Programs, Space Complexity, Combinatorics}
}
05.03.2014
Keywords: 

Lower bounds, Branching Programs, ReadOnce Branching Programs, Space Complexity, Combinatorics 
Seminar: 

31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)

Issue date: 

2014 
Date of publication: 

05.03.2014 