@article{Arnborg1993AnAT,
title={An Algebraic Theory of Graph Reduction},
author={Stefan Arnborg and Bruno Courcelle and Andrzej Proskurowski and Detlef Seese},
journal={J. ACM},
year={1993},
volume={40},
pages={1134-1164}
}

Wc show how membership in classes of graphs definable m monwhc second-order ]oglc and of bounded treewldth can be decided by finite sets of terminating reduction rules. The method is constructive in the sense that wc describe an algorlthm that wdl produce, from J formula in monxhc second-order Ioglc and an mleger k such that the class dcfmed by the formul~ IS of treewidth s k, a set of rewrite rules that rcducxs any member of the elms to one of’ firrltely many graphs, in a number of steps… CONTINUE READING