Affiliation:
1. University of Siegen, Germany
Abstract
We present a general framework for balancing expressions (terms) in the form of so-called tree straight-line programs. The latter can be seen as circuits over the free term algebra extended by contexts (terms with a hole) and the operations, which insert terms/contexts into contexts. In Ref. [16], it was shown that one can compute for a given term of size
n
in logspace a tree straight-line program of depth
O
(log
n
) and size
O
(
n
/ log
n
). In the present article, it is shown that the conversion can be done in DLOGTIME-uniform TC
0
. This allows reducing the term evaluation problem over an arbitrary algebra A to the term evaluation problem over a derived two-sorted algebra
F
(
A
). Three applications are presented: (i) an alternative proof for a recent result by Krebs et al. [25] on the expression evaluation problem is given; (ii) it is shown that expressions for an arbitrary (possibly non-commutative) semiring can be transformed in DLOGTIME-uniform TC
0
into equivalent circuits of logarithmic depth and size
O
(
n
/ log
n
); and, (iii) a corresponding result for regular expressions is shown.
Publisher
Association for Computing Machinery (ACM)
Subject
Computational Theory and Mathematics,Theoretical Computer Science
Cited by
2 articles.
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