English

The complexity of normal form rewrite sequences for Associativity

cmp-lg 2008-02-03 v2 Computation and Language

Abstract

The complexity of a particular term-rewrite system is considered: the rule of associativity (x*y)*z --> x*(y*z). Algorithms and exact calculations are given for the longest and shortest sequences of applications of --> that result in normal form (NF). The shortest NF sequence for a term x is always n-drm(x), where n is the number of occurrences of * in x and drm(x) is the depth of the rightmost leaf of x. The longest NF sequence for any term is of length n(n-1)/2.

Keywords

Cite

@article{arxiv.cmp-lg/9406030,
  title  = {The complexity of normal form rewrite sequences for Associativity},
  author = {Michael Niv},
  journal= {arXiv preprint arXiv:cmp-lg/9406030},
  year   = {2008}
}

Comments

5 pages

R2 v1 2026-07-22T09:57:47.228Z