This paper analyzes the proof-theoretic strength of an infinite version of several theorems from algorithmic graph theory. In particular, theorems on reachability matrices, shortest path matrices, topological sorting, and minimal spanning trees are considered.
Working in the framework of reverse mathematics, we consider representations of reals as rapidly converging Cauchy sequences, decimal expansions, and two sorts of Dedekind cuts. Converting single reals from one representation to another can always be carried out in RCA₀. However, the conversion process is not always uniform. Converting infinite sequences of reals in some representations to other representations requires the use of WKL₀ or ACA₀.
Page 1