The computational complexity of the unconstrained limited domino problem (with implications for logical decision problems)

  • Martin Fürer
Section IV: Decision Problems
Part of the Lecture Notes in Computer Science book series (LNCS, volume 171)


The unconstrained domino or tiling problem is the following. Given a finite set T (of tiles), sets H,VT×T and a cardinal kω, does there exist a function :k×k->T such that (t(i,j),t(i+1,j))εH and (t(i,j),t(i,j+1))εV for all i,j<k ?

The unlimited domino problem (k infinite) has played an important role in the process of finding the undecidability proof for the ∀ε∀ prefix class of predicate calculus. The limited domino problem is similarly connected to some decidable prefix classes.

The limited domino problem is NP-complete, if k is given in unary. The same was conjectured for k given in binary, but we show an Θ (c n ) nondeterministic time lower bound (upper bound O(d n )). As a consequence, the non-deterministic time complexity of the decision problem for the Вε ВВ class of predicate calculus lies between Θ (c n/log n ) and O(d n/log n ).


Filing System Turing Machine Tiling System Binary Number Origin Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Martin Fürer
    • 1
  1. 1.University of ZürichSwitzerland

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