A universal tree balancing theorem [article]

Moses Ganardi, Markus Lohrey
2017 arXiv   pre-print
We present a general framework for balancing expressions (terms) in 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. It is shown that for every term one can compute in DLOGTIME-uniform TC^0 a tree straight-line program of logarithmic depth and size O(n/ n). This allows reducing the term evaluation problem over an arbitrary algebra A
more » ... the term evaluation problem over a derived two-sorted algebra F(A). Several applications are presented: (i) an alternative proof for a recent result by Krebs, Limaye and Ludwig 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/ n), and (iii) a corresponding result for regular expressions is shown.
arXiv:1704.08705v3 fatcat:ww45wpahx5axvd2wkxvfwqppci