The Complexity of the Diagonal Problem for Recursion Schemes

Pawel Parys, Marc Herbstritt
2018 Foundations of Software Technology and Theoretical Computer Science  
We consider nondeterministic higher-order recursion schemes as recognizers of languages of finite words or finite trees. We establish the complexity of the diagonal problem for schemes: given a set of letters A and a scheme G, is it the case that for every number n the scheme accepts a word (a tree) in which every letter from A appears at least n times. We prove that this problem is (m−1)-EXPTIME-complete for word-recognizing schemes of order m, and m-EXPTIME-complete for tree-recognizing schemes of order m.
doi:10.4230/lipics.fsttcs.2017.45 dblp:conf/fsttcs/Parys17 fatcat:vultckgqabh7tbpjepoirksrxi