The Distance Function on a Computable Graph

Document Type

Conference Proceeding

Publication Date



We apply the techniques of computable model theory to the distance function of a graph. This task leads us to adapt the definitions of several truth-table reducibilities so that they apply to functions as well as to sets, and we prove assorted theorems about the new reducibilities and about functions which have nonincreasing computable approximations. Finally, we show that the spectrum of the distance function can consist of an arbitrary single bttdegree which is approximable from above, or of all such btt-degrees at once, or of the bT-degrees of exactly those functions approximable from above in at most n steps.


This work is a pre-print version of the conference proceeding: Calvert, W., Miller, R., Chubb, J. Approximating functions and measuring distance on a graph (2013). In R. Downey, J. Brendle, R. Goldblatt, K. Byunghan (Eds.), Proceedings of the 12th Asian Logic Conference (pp. 24-52). Singapore: World Scientific Publishing Company.