Constraint Logic: A Uniform Framework for Modeling Computation as Games
CCC '08 Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity
Undirected connectivity in log-space
Journal of the ACM (JACM)
Games, Puzzles, and Computation
Games, Puzzles, and Computation
Planar and Grid Graph Reachability Problems
Theory of Computing Systems - Special Issue: Computation and Logic in the Real World; Guest Editors: S. Barry Cooper, Elvira Mayordomo and Andrea Sorbi
Relationships between nondeterministic and deterministic tape complexities
Journal of Computer and System Sciences
Grid graphs with diagonal edges and the complexity of xmas mazes
FUN'12 Proceedings of the 6th international conference on Fun with Algorithms
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We investigate the computational complexity of two maze problems, namely rolling block and Alice mazes. Simply speaking, in the former game one has to roll blocks through a maze, ending in a particular game situation, and in the latter one, one has to move tokens of variable speed through a maze following some prescribed directions. It turns out that when the number of blocks or the number of tokens is not restricted (unbounded), then the problem of solving such a maze becomes PSPACE-complete. Hardness is shown via a reduction from the nondeterministic constraint logic (NCL) of [E. D. Demaine, R. A. Hearn: A uniform framework or modeling computations as games. Proc. CCC, 2008] to the problems in question. By using only blocks of size 2×1×1, and no forbidden squares, we improve a previous result of [K. Buchin, M. Buchin: Rolling block mazes are PSPACE-complete. J. Inform. Proc., 2012] on rolling block mazes to best possible. Moreover, we also consider bounded variants of these maze games, i.e., when the number of blocks or tokens is bounded by a constant, and prove close relations to variants of graph reachability problems.