Some Combinatorial Game Problems Require Ω(nk) Time

Abstract

The first “natural” languages are established as solvable m deterministic polynomial time, for the recogmtion of which polynomial-time lower bounds can be shown. The k-pebble game problem Is to determine whether the first player has a forced win in the pebble game using only k pebbles. The main result of this paper is that the k-pebble game problem requires Ω(n(k-1)/4-1) time for its recogmUon on multitape Tunng machines for any. The problem is solvable m deterministic polynomial time. Then we consider other combinatorial game problems that also have nontrivlal polynomial deterministic lower time bounds. © 1984, ACM. All rights reserved.