On the Tree Width of Ada Programs

The tree width of a graph G measures how close G is to being a tree or a series-parallel graph. Many well-known problems that are otherwise NP-complete can be solved efficiently if the underlying graph structure is restricted to one of fixed tree width. In this paper we prove that the tree width of goto-free Ada programs without labeled loops is ≤ 6. In addition we show that both the use of gotos and the use of labeled loops can result in unbounded tree widths of Ada programs. The latter result suggested to study the tree width of actual Ada programs. We implemented a tool capable of calculating tight upper bounds of the tree width of a given Ada program efficiently. The results show that most existing Ada code has small tree width and thus allows efficient automatic static analysis for many well-known problems and – as a by-product – most Ada programs are very close to series-parallel programs.